Showing papers on "Cancellative semigroup published in 1993"
TL;DR: A semilattice of simple poe -semigroups is defined in this article as an ordered semigroup having a greatest element, that is, an ordered order semigroup (:po -semigroup) having the greatest element.
Abstract: -semigroup -that is an ordered semigroup (:po -semigroup) having a greatest element - is a semilattice of simple semigroups if and only if it is a semilattice of simple poe -semigroups [3].
50 citations
TL;DR: In this article, it was shown that any countably compact, cancellative topological semigroup with any additional condition that would imply sequential compactness is also a topological group.
Abstract: . Some results of Mukherjea and Tserpes are generalized by showing that any sequentially compact, cancellative topological semigroup is a topological group. Hence, any countably compact, cancellative topological semigroup with any additional condition that would imply sequential compactness is also a topological group. Finally, it is shown that any w-bounded, cancellative topological semigroup is also a topological group.
18 citations
TL;DR: A semigroup with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S, (3t G T)(Vu, v 6 T) tt* = uv' => u = v. as discussed by the authors.
Abstract: A semigroup 5 with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S, (3t G T)(Vu, v 6 T) tt* = uv' => u = v. It is shown that a semigroup is inverse if and only if it is a special involution semigroup in which every element invariant under the involution is periodic. Other examples of special involution semigroups are discussed; these include free semigroups, totally ordered cancellative commutative semigroups and certain semigroups of matrices. Some properties of the semigroup algebras of special involution semigroups are also derived. In particular, it is shown that their real and complex semigroup algebras are semiprimitive. 1. DEFINITIONS
12 citations
TL;DR: In this paper, it was shown that the Gelfand-Kirillov dimension is finite whenever it is finite on all cancellative subsemigroups of a semigroup.
8 citations
TL;DR: In this paper, the authors considered the problem of finding a description of semigroup rings over a field K that are semiprime or prime, where the description involves the FC-centre of G defined as the subset of all elements with finitely many conjugates in G.
Abstract: Let S be a cancellative semigroup. This paper is motivated by the problem of finding a description of semigroup rings K [ S ] over a field K that are semiprime or prime. Results of this type are well-known in the case of a group ring K [ G ], cf. [8]. The description, as well as the proofs, involve the FC-centre of G defined as the subset of all elements with finitely many conjugates in G . In [4], [5] Krempa extended the FC-centre techniques to the case of an arbitrary cancellative semigroup S . He defined a subsemigroup Δ( S ) of S which coincides with the FC-centre in the case of groups, and can be used to describe the centre and to study special elements of K [ S ]. His results were strengthened by the author in [7], where Δ( S ) was also applied in the context of prime and semiprime algebras K [ S ]. However, Δ( S ) itself is not sufficient to characterize semigroup rings of this type. We note that in [2], [3] Dauns developed a similar idea for a study of the centre of semigroup rings and certain of their generalizations.
6 citations
5 citations
TL;DR: A semigroup S has property P ∗ n, n ⩾ 2, if, given elements x i,…, x n of S, at least two of the n! products of these elements coincide, and is proved to have property P∗ 4.
3 citations
2 citations
TL;DR: In this article, it was shown that a completely regular semigroup is in the semigroup variety generated by the bicyclic semigroup if and only if it is an orthogroup whose maximal subgroups are abelian.
Abstract: We shall show that a completely regular semigroup is in the semigroup variety generated by the bicyclic semigroup if and only if it is an orthogroup whose maximal subgroups are abelian. Therefore the lattice of subvarieties of the variety generated by the bicyclic semigroup contains as a sublattice a countably infinite distributive lattice of semigroup varieties, each of which consists of orthogroups with maximal subgroups that are torsion abelian groups. In particular, every band divides a power of the bicyclic semigroup.
2 citations
TL;DR: In this article, the infinitesimal generator of the semigroup is found by differentiating at t = 0, and the type of limit is epigraphical convergence in a uniform sense.
Abstract: The Lagrange problem in the calculus of variations exhibits the principle of optimality in a particularly simple form. The binary operation of inf-composition applied to the value functions of a Lagrange problem equates the principle of optimality with a semigroup property. This paper finds the infinitesimal generator of the semigroup by differentiating at t = 0. The type of limit is epigraphical convergence in a uniform sense. Moreover, the extent to which a semigroup is uniquely determined by its infinitesimal generator is addressed
2 citations
TL;DR: In particular, if a semigroup varietyV contains the variety of commutative three-nilpotent semigroups, or if it is a variety of bands containing all semilattices, then, for any A∈V and any left cancellative monoidM, there is a semigroupS ∈ V such that A is a retract of S and M is isomorphic to the monoid of all injective endomorphisms of S as mentioned in this paper.
Abstract: If a semigroup varietyV contains the variety of commutative three-nilpotent semigroups, or if it is a variety of bands containing all semilattices, then, for anyA∈V and any left cancellative monoidM, there is a semigroupS∈V such thatA is a retract ofS andM is isomorphic to the monoid of all injective endomorphisms ofS.
01 Jan 1993
TL;DR: In this article, the second adjoint of a Co-semigroup of linear operators on a Banach space X is shown to be strongly continuous for t > O, resp. t > 0.
Abstract: Let T(t) be a Co-semigroup of linear operators on a Banach space X, and let X@, resp. X( , denote the closed subspaces of X* consisting of all functionals x* such that the map t 4 T*(t)x* is strongly continuous for t > O, resp. t > O. Theorem. Every nonzero orbit of the quotient semigroup on X*/X? is nonseparably valued. In particular, orbits in X*/XO are either zero for t > 0 or nonseparable. It also follows that the quotient space X* /X? is either zero or nonseparable. If T(t) extends to a Co-group, then X*I/X is either zero or nonseparable. For the proofs we make a detailed study of the second adjoint of a Cosemigroup.