Showing papers on "Cancellative semigroup published in 2005"
TL;DR: On the infinite semigroup of matrix units, there exists no semigroup compact [countably compact] topology, and any continuous homomorphism from the infinite topological matrix units into a compact topological semigroup is annihilating.
Abstract: On the infinite semigroup of matrix units there exists no semigroup compact [countably compact] topology. Any continuous homomorphism from the infinite topological semigroup of matrix units into a compact topological semigroup is annihilating. The semigroup of matrix units is algebraically h-closed in the class of topological inverse semigroups. Some H-closed minimal semigroup topologies on the infinite semigroup of matrix units are considered.
44 citations
TL;DR: It is proved here that $\mathbf{B^1_2}$, the six-element Perkins semigroup, has co-NP-complete term-equivalence problem, a result which leads to the completion of the classification of he term-Equivalence problems for monoid extensions of aperiodic Rees matrix semigroups.
Abstract: A semigroup term is a finite word in the alphabet x1, x2,…. The length of a term p, denoted by |p|, is the number of variables in p, including multiplicities. The term-equivalence problem for a finite semigroup S has as an instance a pair of terms {p,q} with size |p| + |q| and asks whether p ≈ q is an identity over S. It is proved here that $\mathbf{B^1_2}$, the six-element Perkins semigroup, has co-NP-complete term-equivalence problem, a result which leads to the completion of the classification of he term-equivalence problems for monoid extensions of aperiodic Rees matrix semigroups. From the main result it follows that there exist finite semigroups with tractable term-equivalence problems but having subsemigroups and homomorphic images with co-NP-complete term-equivalence problems.
29 citations
TL;DR: In this paper, it was shown that a left cancellative semigroup S is left amenable if and only if the Banach algebra l 1(S) is approximately amenable.
Abstract: In the present paper, it is shown that a left cancellative
semigroup S (not necessarily with identity) is left amenable
whenever the Banach algebra l1(S) is approximately amenable. It is also proved that if S is a Brandt semigroup over a group
G with an index set I, then l1(S) is approximately
amenable if and only if G is amenable. Moreover l1(S) is amenable if and only if G is amenable and I is finite. For a
left cancellative foundation semigroup S with an identity such
that for every Ma(S)-measurable subset B of S
and s ∈ S the set sB is Ma(S)-measurable,
it is proved that if the measure algebra Ma(S) is approximately
amenable, then S is left amenable. Concrete examples are given
to show that the converse is negative.
26 citations
TL;DR: In this paper, the weak module amenability of Banach algebras over another Banach algebra with compatible actions has been studied, and it has been shown that the semigroup algebra of a commutative inverse semigroup is always weakly amenable as a module over its subsemigroup of idempotents.
Abstract: We study the weak module amenability of Banach algebras which are Banach module over another Banach algebra with compatible actions. As an example we show that the semigroup algebra of a commutative inverse semigroup is always weakly amenable as a module over the semigroup algebra of its subsemigroup of idempotents.
26 citations
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TL;DR: The notion of Connes-amenability for dual Banach algebras, as introduced by Runde, was investigated in this paper for bidual algebra and weighted semigroup algebra.
Abstract: We investigate the notion of Connes-amenability for dual Banach algebras, as introduced by Runde, for bidual algebras and weighted semigroup algebras. We provide some simplifications to the notion of a $\sigma WC$-virtual diagonal, as introduced by Runde, especially in the case of the bidual of an Arens regular Banach algebra. We apply these results to discrete, weighted, weakly cancellative semigroup algebras, showing that these behave in the same way as C$^*$-algebras with regards Connes-amenability of the bidual algebra. We also show that for each one of these cancellative semigroup algebras $l^1(S,\omega)$, we have that $l^1(S,\omega)$ is Connes-amenable (with respect to the canonical predual $c_0(S)$) if and only if $l^1(S,\omega)$ is amenable, which is in turn equivalent to $S$ being an amenable group. This latter point was first shown by Gr{\"o}nb\ae k, but we provide a unified proof. Finally, we consider the homological notion of injectivity, and show that here, weighted semigroup algebras do not behave like C$^*$-algebras.
23 citations
TL;DR: It is proved that any small cancellative category admits a faithful functor to a cancellative monoid and this result is used to show that any primitive ample semigroup is a full subsemigroup of a Rees matrix semigroup.
Abstract: We prove that any small cancellative category admits a faithful functor to a cancellative monoid. We use our result to show that any primitive ample semigroup is a full subsemigroup of a Rees matrix semigroup where M is a cancellative monoid and P is the identity matrix. On the other hand a consequence of a recent result of Steinberg is that it is undecidable whether a finite ample semigroup embeds as a full subsemigroup of an inverse semigroup.
19 citations
TL;DR: In this paper, a solution to the Diophantine Frobenius problem for pseudo-symmetric numerical semigroups with embedding dimension three is given, and a presentation for this kind of semigroup and a formula to determine whether or not such a numerical semigroup is pseudo symmetric is given.
19 citations
TL;DR: In this article, the hypercyclicity of the translation group on the weighted spaces was shown to be Ω(L^p_\rho(\mathbb R,\mathbb C)$ for admissible weight.
Abstract: In this note we extend the hypercyclicity
criterion (HC) to $C_0$- semigroups on separable Banach spaces and
characterize semigroups satisfying (HC). Using (HC) we show the
hypercyclicity of the translation group on the weighted spaces
$L^p_\rho(\mathbb R,\mathbb C)$ or $C_{0,\rho}(\mathbb R,\mathbb C)$ for admissible weight
functions $\rho$.
16 citations
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TL;DR: In this article, pairwise non-isomorphic semigroups obtained from the finite inverse symmetric semigroup and the bicyclic semigroup were classified by Ljapin's deformed multiplication.
Abstract: Pairwise non-isomorphic semigroups obtained from the finite inverse symmetric semigroup $\mathcal{IS}_n ,$ finite symmetric semigroup $\mathcal{T}_n$ and bicyclic semigroup by the deformed multiplication proposed by Ljapin are classified.
16 citations
TL;DR: The semigroup of values of irreducible space curve singularities is the set of intersection multiplicities among hypersurfaces and the given curve as mentioned in this paper, which is an invariant of the singularity and characterizes the equisingularity type considered by Zariski.
Abstract: The semigroup of values of irreducible space curve singularities is the set of intersection multiplicities among hypersurfaces and the given curve. It is an invariant of the singularity, and for plane curves it characterizes the equisingularity type considered by Zariski. For space curve singularities the semigroup of values is a numerical semigroup and it can not be computed by means of the exponents of any Puiseux parametrization, as in the plane case. We obtain an algorithm for calculating the semigroup of values of a space curve singularity, which determines the generators of the semigroup and the valuation ideals associated with the semigroup. We give a Maple version of the algorithm.
11 citations
TL;DR: In this article, the structure of any congruence of a permutable inverse semigroup of finite rank is described, i.e., any permutable semigroup can be described as a permutation of a semigroup.
Abstract: We describe the structure of any congruence of a permutable inverse semigroup of finite rank.
TL;DR: For every semigroup of finite exponent whose chains of idempotents are uniformly bounded, the authors constructs an identity which holds on this semigroup but does not hold on the variety of all idempots.
Abstract: For every semigroup of finite exponent whose chains of idempotents are
uniformly bounded we construct an identity which holds on this semigroup but
does not hold on the variety of all idempotent semigroups. This shows that the
variety of all idempotent semigroups E is not contained in any finitely generated
variety of semigroups. Since E is locally finite and each proper subvariety of E is
finitely generated [1, 3, 4], the variety of all idempotent semigroups is a minimal
example of an inherently non-finitely generated variety.
TL;DR: In this article, the construction theorem of regular F-abundant semigroups is obtained, and it is shown that a regular Fabi-convex semigroup is embeddable into a semidirect product of a regular band by a cancellative monoid.
Abstract: The investigation of regular F-abundant semigroups is initiated. In fact, F-abundant semigroups are generalizations of regular cryptogroups in the class of abundant semigroups. After obtaining some properties of such semigroups, the construction theorem of the class of regular F-abundant semigroups is obtained. In addition, we also prove that a regular F-abundant semigroup is embeddable into a semidirect product of a regular band by a cancellative monoid. Our result is an analogue of that of Gomes and Gould on weakly ample semigroups, and also extends an earlier result of O'Carroll on F-inverse semigroups.
TL;DR: For a commutative cancellative semigroup S, the authors defined the rank of S intrinsically and characterized the rank in terms of embeddability into a rational vector space of the greatest power cancellative image of S.
Abstract: For a commutative cancellative semigroup S , we define the rank of S intrinsically. This definition implies that the rank of S equals the usual rank of its group of quotients. We also characterize the rank in terms of embeddability into a rational vector space of the greatest power cancellative image of S.
TL;DR: In this article, it was shown that weak compactness of partial orbits is a necessary and sufficient condition for strong continuity of the restriction of a C0-semigroup, and that if the embedded Banach space is reflexive and the norms of the restricted semigroup operators are bounded near the initial time, then the restriction is strongly continuous.
Abstract: A linear semigroup in a Banach space induces a linear semigroup on a Banach space that can be continuously embedded in the former such that its image is invariant. This restriction need not be strongly continuous, although the original semigroup is strongly continuous. We show that norm or weak compactness of partial orbits is a necessary and sufficient condition for strong continuity of the restriction of a C0-semigroup. We then show that if the embedded Banach space is reflexive and the norms of the restricted semigroup operators are bounded near the initial time, then the restricted semigroup is strongly continuous.
TL;DR: In this article, it was shown that a mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with the normal band quotient and cancellative classes.
Abstract: A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.
Journal Article•
TL;DR: A left C-rpp semigroup is defined as a strongly semigronp semigroup such that L~((l)) is a congruence on S; and for all e~2=e∈S,eSSe.
Abstract: A semigroup S is called a left C-rpp semigroup if S is a strongly semigronp such that L~((l)) is a congruence on S;and for all e~2=e∈S,eSSe.The aim of this paper is to study left C-rpp semigroups. Some characterizations of left C-rpp semigroups are established.
24 Feb 2005
TL;DR: In this article, a group G such that G contains a free noncyclic subgroup (hence, G satisfies no group identity) and G, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity is constructed.
Abstract: To solve two problems of Bergman stated in 1981, we construct a group G such that G contains a free noncyclic subgroup (hence, G satisfies no group identity) and G, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity.
Posted Content•
TL;DR: Pairwise non isomorphic semigroups obtained from the semigroup PT_n of all partial transformations by the deformed multiplication proposed by Ljapin are classified in this paper.
Abstract: Pairwise non isomorphic semigroups obtained from the semigroup PT_n of all partial transformations by the deformed multiplication proposed by Ljapin are classified.
TL;DR: In this article, it was shown that S (C ) contains a copy of the bifree locally inverse semigroup, if C is a group on X and S(C ) is a completely simple semigroup on X.
TL;DR: In this article, the authors show that CLn, the chain with n elements, is efficient and that the direct product CLm × CLn is inefficient, and they embed any finitely presented semigroup S into an inefficient semigroup, where SLn is the free semilattice of rank n.
Abstract: In this paper, we show that CLn, the chain with n elements, is efficient and that the direct product CLm × CLn is inefficient. Moreover, we embed any finitely presented semigroup S into an inefficient semigroup, namely, the semigroup S ⋃ SLn, where SLn is the free semilattice of rank n.
TL;DR: In this paper, the authors define a semigroup of linear continuous set-valued functions with an infinitesimal operator, which is a uniformly continuous semigroup majorized by an exponential semigroup.
Abstract: Let {F t : t ≥ 0} be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small t every linear selection of F t is invertible and there exists an exponential semigroup {f t : t ≥ 0} of linear continuous selections f t of F . IfX is a nonempty set, then n(X) denotes the set of all nonempty subsets of X. All linear spaces are over R. We say that a nonempty subset C of a linear space is a cone if tC ⊂ C for every t > 0. Let X, Y be linear spaces and C be a convex cone in X. The set-valued function (abbreviated to s.v. function) F : C→n(Y ) is called superadditive if F (x) + F (y) ⊂ F (x+ y) for all x, y ∈ C. (1) F is said to be additive if equality holds in (1), and Q+-homogeneous if F (λx) = λF (x) for all x ∈ C, λ ∈ Q+, (2) where Q+ is the set of all positive rational numbers. F is linear if it is additive and (2) is satisfied for all λ > 0. IfX is a linear topological space, then b(X) denotes the set of all bounded elements of n(X), and c(X) stands for the family of all compact elements of n(X). Now let X,Y be topological spaces. An s.v. function F : X → n(Y ) is called lower semicontinuous at x0 ∈ X if for every open set G in Y such that F (x0) ∩ G 6= ∅ there exists a neighbourhood U of x0 in X such that F (x) ∩ G 6= ∅ for x ∈ U . We say that F is lower semicontinuous in a set A ⊂ X if F is lower semicontinuous at every point x ∈ A. We say that F : X → n(Y ) is upper semicontinuous at x0 ∈ X if for every open set G ⊂ Y such that F (x0) ⊂ G there exists a neighbourhood U of x
TL;DR: In this article, it was shown that an F-regular semigroup S is isomorphic to a well determined subsemigroup of a semidirect product of a band X by S/σS, where X belongs to the band variety, generated by the band of idempotents ES of S. Theorem 4.
Abstract: A regular (inverse) semigroup S is called F-regular (F-inverse), if each class of the least group congruence σS contains a greatest element with respect to the natural partial order on S. Such a semigroup is necessarily an E-unitary regular (hence orthodox) monoid. We show that each F-regular semigroup S is isomorphic to a well determined subsemigroup of a semidirect product of a band X by S/σS, where X belongs to the band variety, generated by the band of idempotents ES of S. Our main result, Theorem 4, is the regular version of the corresponding fact for inverse semigroups, and might be useful to generalize further features of the theory of F-inverse semigroups to the F-regular case.
01 Jan 2005
TL;DR: Adequate partial semigroups were first intro-duced by Bergelson, Blass, and Hindman as discussed by the authors and they give rise to a semigroup S which is a subset of S. They also show that if S is an adequate countable cancellative semigroup, S contains many copies of H in S.
Abstract: Adequate partial semigroups were rst intro- duced by Bergelson, Blass, and Hindman. They give rise to a semigroup S, which is a subset of S. We extend the Commutative Central Sets Theorem to adequate partial semigroups. We also show that if S is an adequate countable cancellative semigroup, S contains many copies of H in S.
01 Jun 2005
TL;DR: In this article, the act of a semigroup is extended into an ordered semigroup, and the presentation theorems of ordered semiprogroup are developed to characterize quotient and coproduct of R-posets.
Abstract: The act of a semigroup is extended into an ordered semigroup, and develop the presentation theorems of ordered semiproups. The nitions of congruence and R-morphism is introduced to characterize the quotient and coproduct of R-posets.
Journal Article•
TL;DR: In this paper, the transition function is a positive contraction C_0 semigroup on a subspace C 1 of l ∞ and the generator of the Markov integrated semigroup is densely defined in l∞ if and only if q-matrix Q is uniformly bounded.
Abstract: We prove that the transition function is a positive contraction C_0 semigroup on a subspace C1 of l_∞. We obtain that the generator of the Markov integrated semigroup is densely defined in l_∞ if and only if q-matrix Q is uniformly bounded. At the same time, a sufficient and necessary condition for a transition function to a Feller-Reuter-Riley transition function, is also given. Finally, in an ordered Banach space, a generation theorem is obtained for the increasing integrated semigroup of contractions.
TL;DR: In this article, the authors give an example of a tight inverse semigroup which is not bisimple and not congruence-free, but is congruent with a tight semigroup.
Abstract: We give an example of a tight inverse semigroup which is not bisimple and not congruence-free.
TL;DR: In this article, an evolution family whose generator is formed by a time-dependent bounded perturbation of a strongly continuous semigroup was considered and a formula for a variation of a parameter and the corresponding generalization of the Dyson-Phillips theorem was proved.
Abstract: We consider an evolution family whose generator is formed by a time-dependent bounded perturbation of a strongly continuous semigroup. We do not use the condition of the continuity of a perturbation. We prove a formula for a variation of a parameter and the corresponding generalization of the Dyson-Phillips theorem.
TL;DR: In this article, the identity of a group of permutations to the idempotent was identified without loss of generality, and the maximal subsemilattices and the maximum inverse subsemigroup of a near permutation semigroup were characterized.
Abstract: A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group G of permutations on N elements and by a set H of transformations of rank N − 1. For near permutation semigroups S = ≪ G, H ≫, where H is a group, we consider a group of permutations, whose elements are constructed from the elements of H. Without loss of generality, we identify the identity of H to the idempotent . The condition 2 ∉O G(S)(1), where , is a necessary condition for S to be inverse and is a sufficient one for S to be ± bℛ-unipotent. We characterize the subsemilattices and the maximal subsemilattices of the near permutation semigroups satisfying the above condition. With those characterizations of a semilattice E contained in a semigroup S, we determine the maximum inverse subsemigroup of S which has E as its subsemilattice of idempotents. We use this result to test whether a near permutation semigroup is inverse.