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 necessary and sufficient condition for the existence of an orthodox semigroup T with band of idempotents and a greatest inverse semigroup homomorphic image S for every band E and inverse S is given.
Abstract: In the present paper we deal with two problems concerning orthodox semigroups. M. Yamada raised the questions in [6] whether there exists an orthodox semigroup T with band of idempotents E and greatest inverse semigroup homomorphic image S for every band E and inverse semigroup S which have the property that
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is isomorphic to the semilattice of idempotents of S, and if T exists then whether it is always unique up to isomorphism. T. E. Hall [1] has published counter-examples in connection with both questions and, moreover, he has given a necessary and sufficient condition for existence. Now we prove a more effective necessary and sufficient condition for existence and deal with uniqueness, too. On the other hand, D. B. McAlister's theorem in [4] saying that every inverse semigroup is an idempotent separating homomorphic image of a proper inverse semigroup is generalized for orthodox semigroups. The proofs of these results are based on a theorem concerning a special type of pullback diagrams. In verifying this theorem we make use of the results in [5] which we draw up in Section 1. The main theorems are stated in Section 2. For the undefined notions and notations the reader is referred to [2].
20 citations
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01 Jan 2000TL;DR: In this article, the authors gave a new proof of the result of Straubing and Therien that every J-trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1.
Abstract: In this paper we give a new proof of the following result of Straubing and Therien: Every J-trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1.
20 citations
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TL;DR: Weakly ordered semigroups were introduced in this paper, where the radical of the semigroup algebras was computed for weakly ordered semiigroups, which generalizes some results on left regular bands.
Abstract: We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0- Hecke algebras.
20 citations
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TL;DR: In this article, it was shown that a semigroup can be embedded in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an identity to the two-element left zero semigroup.
Abstract: The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an identity to the two-element left zero semigroup. We prove that this quasivariety is on the one hand polynomial time decidable, and on the other minimally non-finitely based. A similar result is obtained for the semigroups embeddable in complex hyperplane semigroups.
20 citations
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20 citations