On a certain sub semigroup of the bicyclic semigroup

Makanjuola, S. O.; Umar, Abdullahi

doi:10.1080/00927879708825870

Cited by 5 publications

(8 citation statements)

References 6 publications

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“…The bicyclic monoid B, defined by the presentation b, c; bc = 1 , is one of the most fundamental semigroups, with many remarkable properties and generalizations; see [1], [2], [5], [8], [9], [12], [13], [15], [16].…”

Section: Introduction and Previous Relevant Resultsmentioning

confidence: 99%

Properties of the subsemigroups of the bicyclic monoid

Descalço

Ruškuc

2008

Czech Math J

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In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B.

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Section: Introduction and Previous Relevant Resultsmentioning

confidence: 99%

Properties of the subsemigroups of the bicyclic monoid

Descalço

Ruškuc

2008

Czech Math J

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“…The semigroup B + and its dual were studied by Makanjuola and Umar [20], who first showed they are ample. Descalço and Ruškuc [4] made a general study of the subsemigroups of B, regarded as a 'plain' semigroup; Descalço and Higgins [5] went on to study those subsemigroups that are 'abundant', which in our context means ample and, therefore, restriction semigroups.…”

Section: Some 'Forbidden' Restriction Semigroupsmentioning

confidence: 99%

On lattices of varieties of restriction semigroups

Jones

2012

Semigroup Forum

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“…Here we know that (1,1)> (2,2)> (3,3)> (4,4)> (5,5) > … is an omega semi group as in [4] because the set of idempotent elements is totally ordered, that is a Chain.…”

Section: Introductionmentioning

confidence: 99%

“…These have played a very important role in the study of Chain as a semi group. See for example [4,7].…”

Section: Introductionmentioning

confidence: 99%

Characterization of Chain as a Regular Semi Group

Kehinde¹,

Makanjuola²

2008

J. of Mathematics and Statistics

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Problem Statement: There are some special classes of semi group namely: regular and eventually regular, abundant, orthodox, quasi-adequate. The objective of this study were to: (i) Define a new class of semi group on a Poset and give related examples (ii) Study and establish conditions that characterized Chain as a regular semi group. Approach: Tests of some of characteristics of semi group like associativity, commutativity, and regular semi group were carried out on this new class. Results: Conditions were obtained that showed it is associative and regular. Conclusion: Hence the results suggest that since Chain is regular, there are many other things we can still do this with class of semi group such as: (i) Whether one can characterize all the Green's equivalences and their starred analogues (ii) Whether one can characterize all the congruencies of the given semi group (iii) Whether one characterize all the subsemigroups of the given semi group.

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On a certain sub semigroup of the bicyclic semigroup

Cited by 5 publications

References 6 publications

Properties of the subsemigroups of the bicyclic monoid

Properties of the subsemigroups of the bicyclic monoid

On lattices of varieties of restriction semigroups

Characterization of Chain as a Regular Semi Group

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