Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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TL;DR: In this paper, a ring of quotients of the semigroup ring R(S) is discussed, where R has a σ-set Σ and S has a set Δ, and where R is an integral domain and S is a commutative cancellative semigroup.
Abstract: A ring of quotients of the semigroup ring R(S) is discussed where R has a σ-set Σ and S has a σ-set Δ. In particular, we study the cases where (1) R is an integral domain and S is a commutative cancellative semigroup, (2) R is a commutative ring and S is a semilattice and (3) R is a commutative ring and S is a Rees matrix semigroup over a semigroup.
3 citations
TL;DR: In this paper, it was shown that there is a ring with a proper involution * in which S is *-embeddable, which is called R[S], the semigroup ring of S over any formally complex ring R; for example ℝ, Ȼ.
Abstract: Let S be an inverse semigroup. We prove that there is a ring with a proper involution * in which S is *-embeddable. The ring will be a natural one, R[S], the semigroup ring of S over any formally complex ring R; for example ℝ, Ȼ.
3 citations
TL;DR: The semigroup of all one-to-one mappings of a set to itself is shown to have the property that every automorphism is inner as discussed by the authors, which is the same as the semigroup for all automorphisms.
Abstract: The semigroup of all onto mappings of a set to itself and the semigroup of all one-to-one mappings of a set to itself are shown to have the property that every automorphism is inner.
3 citations
01 Jan 2008
TL;DR: A right adequate semigroup of type F is a semigroup which is an F-rpp semigroup if and only if it is isomorphic to some F(M,Y) pair.
Abstract: A right adequate semigroup of type F means a right adequate semigroup which is an F-rpp semigroup. We obtain the structure theorem for right adequate semigroups: a semigroup is a right adequate semigroup of type F if and only if it is isomorphic to some F(M,Y), where (M,Y) is an F-pair. As its applications, we establish a structure for adequate semigroups of type F. Our result extends the results on F-inverse semigroups.
3 citations
TL;DR: In this paper, a transparent syntactic algorithm is proposed to decide whether an identity defines a variety of semigroups with completely regular power, and the algorithm is shown to be efficient.
Abstract: We provide a transparent syntactic algorithm to decide whether an identity defines a variety of semigroups with completely regular power.
3 citations