Results 71 to 80 of about 137 (87)

Analogues of the bicyclic semigroup in simple semigroups without idempotents

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1987
SynopsisBy an important theorem of Andersen, any semigroup, containing idempotents, which is simple but not completely simple contains a copy of the bicyclic semigroup B = 〈a, b | ab = 1〉. In this paper the semigroups A = 〈a, b | a2b = a〉 and C = 〈a, b | a2b = a, ab2 = b〉 are shown to play a similar role in various classes of simple semigroups without ...
Peter R. Jones
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Inverse Subsemigroups of the Bicyclic Semigroup

Mathematical Notes, 2020
In the present paper, a complete description of the inverse subsemigroups of the bicyclic semigroup is given. Isomorphism conditions for two inverse subsemigroups are found. From the inverse subsemigroups under consideration, a category is constructed, and the existence of a functor from this category to the category of finite ordered sets of numbers ...
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BICYCLIC SUBSEMIGROUPS IN AMALGAMS OF FINITE INVERSE SEMIGROUPS

International Journal of Algebra and Computation, 2010
It is well known that an inverse semigroup is completely semisimple if and only if it does not contain a copy of the bicyclic semigroup. We characterize the amalgams [S1, S2; U] of two finite inverse semigroups S1, S2whose free product with amalgamation is completely semisimple and we show that checking whether the amalgamated free product of finite ...
Rodaro E.
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Completely regular semigroups in the variety generated by the bicyclic semigroup

Algebra Universalis, 1993
The bicyclic semigroup is a semigroup with identity 1 which can be given by the presentation \(\langle a,b; ab = 1\rangle\). It is shown that the variety generated by the bicyclic semigroup contains a completely regular semigroup iff it is an orthogroup (i.e. its idempotents form a subsemigroup) whose maximal subgroups are abelian.
Francis Pastijn
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DIRICHLET CONVOLUTION, BICYCLIC SEMIGROUP AND A BREAKING PROCESS

International Journal of Number Theory, 2013
The paper deals with certain breaking processes using a compatible partition of a monoid. We introduce the broken Dirichlet convolution and the broken bicyclic semigroup. Both have a common origin and are introduced by the same elementary categorical construction.
Schwab, Emil D.
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Compatible orders on the bicyclic semigroup

Communications in Algebra, 1999
In this paper we determine those compatible partial orders on the bicyclic semigroup B which turn it into a semilatticed semigroup. We shall see that there are exactly four distinct compatible total orderings on B. These are the only compatible orderings which turn B into a lattice ordered semigroup.
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On a Semigroup Generated by the Extended Bicyclic Semigroup and the ω-Closed Family

Journal of Mathematical Sciences, 2023
O. V. Gutik, I. V. Pozdniakova
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On a certain sub semigroup of the bicyclic semigroup

Communications in Algebra, 1997
A Umar
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Null extensions of the bicyclic semigroup $${\varvec{\mathcal {B}}}$$ B are inflations of $${\varvec{\mathcal {B}}}$$ B

Semigroup Forum, 2014
G. T. Clarke, R. A. R. Monzo
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Generalized Bicyclic Semigroups and Jones Semigroups

Southeast Asian Bulletin of Mathematics, 2001
A classic result of Anderson is that if a simple, but not completely simple, semigroup \(S\) contains an idempotent, then it contains a copy of the bicyclic monoid \(B=\langle a,b\mid ab=1\rangle\). The reviewer [Proc. R. Soc. Edinb., Sect. A 106, 11-24 (1987; Zbl 0626.20047)] showed that if such a semigroup is idempotent-free and Green's relation ...
Yu, Bingjun, Jiang, Qifen
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