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, it was shown that a semigroup ring R [S ] has the 2-generator property for large classes of commutative cancellative semigroups.
2 citations
2 citations
TL;DR: In this article, generalized Green's equivalences on all subsemigroups of the bicyclic monoid B were studied and the abundant and adequate subgroups of B were determined.
Abstract: We study generalized Green's equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B.
2 citations
TL;DR: In this paper, the problem of extending a primitive inverse semigroup by another can be reduced to that of extending one Brandt semigroup with only a finite number of idempotents.
Abstract: Every inverse semigroup containing a primitive idempotent is an ideal extension of a primitive inverse semigroup by another inverse semigroup. Consequently, in developing the theory of inverse semigroups, it is natural to study ideal extensions of primitive inverse semigroups (cf. [3; 7]). Since the structure of any primitive inverse semigroup is known, an obvious type of ideal extension to consider is that of one primitive inverse semigroup by another. In this paper, we will construct all such extensions and give an abstract characterization of the resulting semigroup. The problem of extending one primitive inverse semigroup by another can be essentially reduced to that of extending one Brandt semigroup by another Brandt semigroup. The latter problem has been solved by Lallement and Petrich in [3] in case the first Brandt semigroup has only a finite number of idempotents.
2 citations
2 citations