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 article, a large part of the paper is devoted to determining when the Bergman property can be passed from one semigroup to another and vice versa, including the notion of strong co-finality.
Abstract: In this article, we study the Bergman property for semigroups and the associated notions of
cofinality and strong cofinality. A large part of the paper is devoted to determining when the
Bergman property, and the values of the cofinality and strong cofinality, can be passed from
semigroups to subsemigroups and vice versa. Numerous examples, including many important
semigroups from the literature, are given throughout the paper. For example, it is shown
that the semigroup of all mappings on an infinite set has the Bergman property but that its
finitary power semigroup does not; the symmetric inverse semigroup on an infinite set and its
finitary power semigroup have the Bergman property; the Baer�Levi semigroup does not have
the Bergman property.
34 citations
34 citations
TL;DR: In this article, necessary and sufficient conditions for a semigroup identity to hold in the monoid of n × n upper triangular matrices, in terms of equivalence of certain tropical polynomials, were established.
33 citations
33 citations
01 Jan 2001
TL;DR: A survey of recent results on free semigroup algebras can be found in this paper, which are the WOT-closed WO-closed algeses generated by n isometries with pairwise orthogonal ranges.
Abstract: This is a survey of recent results on free semigroup algebras, which are the WOT-closed algebras generated by n isometries with pairwise orthogonal ranges.
33 citations