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Showing papers on "Cancellative semigroup published in 2003"


Journal ArticleDOI
TL;DR: In this paper, it was shown that every lattice can be embedded in the lattice reduct of a cancellative residuated lattice, and there exists an order-preserving injection of all lattice varieties into the subvariety lattice of CanRL.
Abstract: Cancellative residuated lattices are natural generalizations of lattice-ordered groups (� -groups). Although cancellative monoids are defined by quasi-equations, the class CanRL of cancellative residuated lattices is a variety. We prove that there are only two commutative subvarieties of CanRL that cover the trivial variety, namely the varieties generated by the integers and the negative integers (with zero). We also construct examples showing that i nc ontr ast to � -groups, the lattice reducts of cancellative residuated lattices need not be distributive. In fact we prove that every lattice can be embedded in the lattice reduct of a cancellative residuated lattice. Moreover, we show that there exists an order-preserving injection of the lattice of all lattice varieties into the subvariety lattice of CanRL. We define generalized MV-algebras and generalized BL-algebras and prove that the cancellative integral members of these varieties are precisely the negative cones of � -groups, hence the latter form a variety, denoted by LG − .F urthermo re we prove that the map that sends a subvariety of � -groups to the corresponding class of negative cones is a lattice isomorphism from the lattice of subvarieties of LG to the lattice of subvarieties of LG − . Finally, we show how to translate equational bases between corresponding subvarieties, and briefly discuss these results in the context of R. McKenzie's characterization of categorically equivalent varieties.

103 citations


Book ChapterDOI
TL;DR: In this paper, it was shown that a numerical semigroup is pseudo-symmetric if and only if its semigroup ring is a Kunz ring, where the Frobenius number is odd.
Abstract: Symmetric numerical semigroups are probably the numerical semigroups that have been most studied in the literature. The motivation and introduction of these semigroups is due mainly to Kunz, who in his manuscript [44] proves that a onedimensional analytically irreducible Noetherian local ring is Gorenstein if and only if its value semigroup is symmetric. Symmetric numerical semigroups always have odd Frobenius number. The translation of this concept for numerical semigroups with even Frobenius number motivates the definition of pseudo-symmetric numerical semigroups. In [5] it is shown that these semigroups also have their interpretation in one-dimensional local rings, since a numerical semigroup is pseudo-symmetric if and only if its semigroup ring is a Kunz ring.

59 citations


Journal ArticleDOI
TL;DR: In this article, the set of numerical semigroups containing a given numerical semigroup is studied, and characterizations of irreducible numerical semiigroups that unify some of the existing characterizations for symmetric and pseudo-symmetric numerical semiGs are presented.
Abstract: We study the set of numerical semigroups containing a given numerical semigroup. As an application we prove characterizations of irreducible numerical semigroups that unify some of the existing characterizations for symmetric and pseudo-symmetric numerical semigroups. Finally we describe an algorithm for computing a minimal decomposition of a numerical semigroup in terms of irreducible numerical semigroups.

58 citations


Journal ArticleDOI
15 Jan 2003
TL;DR: In this article, it was shown that the automorphisms of the endomorphism semigroup of a free monoid or a free semigroup are either inner or mirror inner.
Abstract: We determine all isomorphisms between the endomorphism semigroups of free monoids or free semigroups and prove that automorphisms of the endomorphism semigroup of a free monoid or a free semigroup are inner or mirror inner. In particular, we answer a question of B. I. Plotkin.

48 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that each weakly E -unitary locally inverse semigroup is embeddable in a restricted semidirect product of a normal band by a completely simple semigroup.

15 citations


Journal ArticleDOI
TL;DR: In this article, the authors prove the κ-tameness of pseudovarieties N, D, K and LI, where κ is the signature comprising semigroup multiplication and the omega implicit operation.
Abstract: Tameness is a strong property of semigroup pseudovarieties related to the membership problem. Let κ be the signature comprising semigroup multiplication and the omega implicit operation. We prove the κ-tameness of the pseudovarieties N, D, K and LI.

15 citations


Journal ArticleDOI
TL;DR: It was shown in this paper that every finite inverse semigroup having only solvable subgroups has no finite basis of identities, unless it is a strict inverse semi-convex semigroup.
Abstract: It is shown that every finite inverse semigroup having only solvable subgroups,viewed as a semigroup with the additional unary operation of inversion, has nofinite basis of identities, unless it is a strict inverse semigroup.

12 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that for every finite weakly left ample semigroup S, there is a finite proper (2, 1)-subalgebra of S and an onto morphism from S to S which separates idempotents.
Abstract: Weakly left ample semigroups are a class of semigroups that are (2,1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories In this paper we show that for every finite weakly left ample semigroup S, there is a finite proper weakly left ample semigroup Ŝ and an onto morphism from Ŝ to S which separates idempotents In fact, Ŝ is actually a (2,1)-subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A)

11 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied algebraic structure of submeans on certain spaces of bounded real valued functions on a semigroup and found local conditions on these spaces in terms of submean for the existence of a left invariant mean.
Abstract: The purpose of this paper is to study some algebraic structure of submeans on certain spaces $X$ of bounded real valued functions on a semigroup and to find local conditions on $X$ in terms of submean for the existence of a left invariant mean.

10 citations


01 Jan 2003
TL;DR: In this article, it is shown that two algebroid branches R and T are equivalent if and only if their Arf closures have the same value semigroup, which is an Arf numerical semigroup and can be expressed in terms of a finite set of information, a set of characters of the branch.
Abstract: Two algebroid branches are said to be equivalent if they have the same multiplicity sequence It is known that two algebroid branches R and T are equivalent if and only if their Arf closures, R and T ′ have the same value semigroup, which is an Arf numerical semigroup and can be expressed in terms of a finite set of information, a set of characters of the branch We extend the above equivalence to algebroid curves with d > 1 branches An equivalence class is described, in this more general context, by an Arf semigroup, that is not a numerical semigroup, but is a subsemigroup of N We express this semigroup in terms of a finite set of information, a set of characters of the curve, and apply this result to determine other curves equivalent to a given one AMS subject classification: 13H15, 14B05

10 citations


Journal ArticleDOI
TL;DR: The structure of the flow monoid of a regular semigroup is studied, which is a category in which every morphism is invertible and determined in terms of the Green relations on the original semigroup.
Abstract: We study the structure of the flow monoid of a regular semigroup. This arises from the approach of Nambooripad of considering a regular semigroup as a groupoid – a category in which every morphism is invertible. A flow is then a section to the source map in this groupoid, and the monoid structure of the set of all flows is determined in terms of the Green relations on the original semigroup.

Journal ArticleDOI
TL;DR: In this article, it was shown that there exists a finitely generated, left amenable semigroup which is right cancellative but not left cancellative, which resolves negatively a question raised by M. Klawe.
Abstract: It is shown that there exists a finitely generated, left amenable semigroup whichis right cancellative but not left cancellative. This resolves negatively a questionraised by M. Klawe.

Journal ArticleDOI
TL;DR: In this paper, the authors give some semigroup characterizations for implicative BCK-algebras and prove that the adjoint semigroups are residualed semigroup.
Abstract: We give some semigroup characterizations for implicative BCK-algebras, and prove that the adjoint semigroups of implicative BCK-algebras are residualed semigroups.

Journal ArticleDOI
TL;DR: In this paper, the enveloping semigroup of a flow generated by the action of a semitopological semigroup on any of its semigroup compactifications is considered, and the possibility of its being one of the known semigroup Compactifications again is explored.
Abstract: We consider the enveloping semigroup of a flow generated by the action of a semitopological semigroup on any of its semigroup compactifications and explore the possibility of its being one of the known semigroup compactifications again. In this way, we introduce the notion of E-algebra, and show that this notion is closely related to the reductivity of the semigroup compactification involved. Moreover, the structure of the universal Eℱ-compactification is also given.

Journal ArticleDOI
TL;DR: In this article, the cardinality of the order relation of a cyclic semigroup is estimated and cyclic sub-semigroups in a finite ordered semigroup are examined, showing that a partially ordered cyclic semiigroup has a spiral structure which leads to a separation of three classes of such semigroups.
Abstract: This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.

Journal ArticleDOI
TL;DR: In this article, it was proved that RS is radical in the sense of Jacobson and if the element 1 has infinite additive order, then S is a locally finite nilsemigroup.
Abstract: Let R be an associative ring with unit, let S be a semigroup with zero, and let RS be a contracted semigroup ring. It is proved that if RS is radical in the sense of Jacobson and if the element 1 has infinite additive order, then S is a locally finite nilsemigroup. Further, for any semigroup S, there is a semigroup T ⊃ S such that the ring RT is radical in the Brown--McCoy sense. Let S be the semigroup of subwords of the sequence abbabaabbaababbab..., and let F be the two-element field. Then the ring FS is radical in the Brown--McCoy sense and semisimple in the Jacobson sense.

Journal ArticleDOI
TL;DR: Using semigroup techniques, this paper obtained solutions of the differential equation (1) using spectral properties of the Gaussian semigroup in order to solve (1), where (B, D) is the generator of a C 0-semigroup on a normalized Banach space.
Abstract: Using semigroup techniques we obtain solutions of the differential equation $$ (1)\qquad u^{\prime\prime}(s) = -Bu(s) + f(s)\;\; \textrm{for}\;\; f \in C_{0}(\mathbb{R},\; X)\;\; \textrm{and}\;\; s \in \mathbb{R}, $$ where (B, D(B)) is the generator of a C 0-semigroup $(T(t))_{t \geq 0}$ on a Banach space X. The main idea is to study a semigroup on $C_{0}(\mathbb{R},\; X)$ given as the product of the Gaussian semigroup and the multiplication semigroup induced by $(T(t))_{t \geq 0}$. We use spectral properties of this semigroup in order to solve (1).