Special subgroups of regular semigroups

T. S. Blyth; M. H. Almeida Santos

doi:10.1080/00927872.2016.1262385

Special subgroups of regular semigroups

T. S. Blyth, M. H. Almeida Santos

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.

Original language	English
Pages (from-to)	4246-4256
Number of pages	11
Journal	Communications in Algebra
Volume	45
Issue number	10
Early online date	1 Dec 2016
DOIs	https://doi.org/10.1080/00927872.2016.1262385
Publication status	Published - 3 Oct 2017

Keywords

Quasi-ideal
Regular semigroup
Special subgroup

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10.1080/00927872.2016.1262385

Blyth_2016_CiA_specialsubgroups_AAM
© 2017, Taylor & Francis. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.tandfonline.com / http://dx.doi.org/10.1080/00927872.2016.1262385
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Cite this

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AU - Blyth, T. S.

AU - Almeida Santos, M. H.

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PY - 2017/10/3

Y1 - 2017/10/3

N2 - Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.

AB - Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.

KW - Quasi-ideal

KW - Regular semigroup

KW - Special subgroup

U2 - 10.1080/00927872.2016.1262385

DO - 10.1080/00927872.2016.1262385

M3 - Article

SN - 0092-7872

VL - 45

SP - 4246

EP - 4256

JO - Communications in Algebra

JF - Communications in Algebra

IS - 10

ER -

Special subgroups of regular semigroups

Abstract

Keywords

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