Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this paper, the Jacobson radical of a semigroup ring R [S ] of a commutative semigroup S is determined when S is S -homogeneous, i.e.
7 citations
••
TL;DR: The relation γ is the smallest equivalence relation on S so that S/γ* is a commutative semigroup and a neighbourhood system for each element of S is defined.
Abstract: Let S be a semigroup. We consider the relation γ and its transitive closure γ*. The relation γ is the smallest equivalence relation on S so that S/γ* is a commutative semigroup. Based on the relation γ, we define a neighbourhood system for each element of S, and we present a general framework of the study of approximations in semigroups. The connections between semigroups and operators are examined.
7 citations
••
TL;DR: In this article, a natural equivalence 6 on the lattice of congruences of a semigroup S of S is studied, and it is shown that 0 is a congruence, each 0-class is a complete sublattice of A(S), and the maximum element in each 0 class is determined.
Abstract: A natural equivalence 6 on the lattice of congruences A(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that 0 is a congruence, each 0-class is a complete sublattice of A(S)-and the maximum element in each 0-class is determined.
7 citations
••
TL;DR: It is shown that the growth function of its balls behaves asymptotically like l(alpha), for alpha = 1 + log 2/log 1+root 5/2 ; that the semigroup satisfies the identity g(6) = g(4); and that its lattice of two-sided ideals is a chain.
Abstract: We consider a very simple Mealy machine ( two nontrivial states over a two-symbol alphabet), and derive some properties of the semigroup it generates. It is an infinite, finitely generated semigroup, and we show that the growth function of its balls behaves asymptotically like l(alpha), for alpha = 1 + log 2/log 1+root 5/2 ; that the semigroup satisfies the identity g(6) = g(4); and that its lattice of two-sided ideals is a chain.
7 citations
••
TL;DR: For the class of completely semisimple inverse semigroups, Goberstein this article showed that any isomorphism that restricts to a bijection on the semilattice of idempotents of a semigroup must be an anisomorphism on its own lattice.
Abstract: An ${\\cal L}$-isomorphism between inverse semigroups $S$ and $T$ is an isomorphism between their lattices ${\\cal L}(S)$ and ${\\cal L}(T)$ of inverse subsemigroups. The author and others have shown that if $S$ is aperiodic – has no nontrivial subgroups – then any such isomorphism $\\Phi$ induces a bijection $\\phi$ between $S$ and $T$. We first characterize the bijections that arise in this way and go on to prove that under relatively weak ‘archimedean’ hypotheses, if $\\phi$ restricts to an isomorphism on the semilattice of idempotents of $S$, then it must be an isomorphism on $S$ itself, thus generating a result of Goberstein. The hypothesis on the restriction to idempotents is satisfied in many applications. We go on to prove theorems similar to the above for the class of completely semisimple inverse semigroups.
7 citations