Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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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.
4 citations
Journal Article•
TL;DR: In this paper, the concept of a proper cover of a right type B semigroup is introduced, and it is proved that any proper cover for a B-Semigroup is a proper covering over a left cancellative monoid.
Abstract: The concept of a proper cover of a right type B semigroup is introduced.Furthermore,it is proved that any proper cover for a right type B semigroup is a proper cover over a left cancellative monoid.A structure theorem of proper covers for a right type B semigroup is also given.
4 citations
TL;DR: In this article, it was shown that the full transformation semigroup T ∃(X) is not abundant if X/E is infinite, and the semigroup is a subsemigroup of.
Abstract: Let be the full transformation semigroup on a nonempty set X and E be an equivalence relation on X. We write Then T∃(X) is a subsemigroup of . In this paper, we proved that the semigroup T∃(X) is not abundant if X/E is infinite.
4 citations
TL;DR: In this paper, it was shown that the semigroup algebra of a U-semiabundant semigroup with Rees matrix semigroups over monoids is a cellular algebra if and only if all of the monoid algebras are cellular.
Abstract: In this paper, we study the cellularity of some semigroup algebras. We show that the semigroup algebra of a U-semiabundant semigroup with Rees matrix semigroups over monoids as its principal \(\sim _U\)-factors is a cellular algebra if and only if all of the monoid algebras are cellular. We also study the cellularity of the semigroup algebra of a semilattice of Rees matrix semigroups. As consequences, we get the cellularity of super abundant semigroup algebras and complete regular semigroup algebras.
4 citations
TL;DR: The semigroup of quotients Q corresponding to an arbitrary right quotient filter on a semigroup S is also a semilattice of groups as mentioned in this paper, which is a regular semigroup in which all idempotents are central.
Abstract: Let S be a semigroup with zero which is a semilattice of groups. In [6], McMorris showed that the semigroup of quotients Q=Q(S) corresponding to the filter of “dense” right ideals of the semigroup S is also a semilattice of groups. He accomplished this by noting that Q is a regular semigroup in which all idempotents are central, an equivalent formulation of a semilattice of groups. In this paper we develop the semigroup of quotients Q corresponding to an arbitrary right quotient filter on S (as defined herein) and note the above result in this more general setting by explicitly constructing a semigroup which is isomorphic to Q. We also see that the underlying semilattice for Q in this case is isomorphic to a semigroup of quotients of the original semilattice for the semigroup S.
4 citations