Volume 33, Issue 2
$\cal P$-Congruence-Free Epigroups

Commun. Math. Res., 33 (2017), pp. 97-109.

Published online: 2019-11

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• Abstract

Let $\cal P$ denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any  congruence either  contains $\cal P$ or its join with $\mathcal P$ is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.

• Keywords

congruence, epigroup, completely 0-simple semigroup

20M10

liujingguo@lyu.edu.cn (Jingguo Liu)

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@Article{CMR-33-97, author = {Liu , Jingguo and Zhang , Jinling}, title = {$\cal P$-Congruence-Free Epigroups}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {33}, number = {2}, pages = {97--109}, abstract = {

Let $\cal P$ denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any  congruence either  contains $\cal P$ or its join with $\mathcal P$ is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2017.02.01}, url = {http://global-sci.org/intro/article_detail/cmr/13410.html} }
TY - JOUR T1 - $\cal P$-Congruence-Free Epigroups AU - Liu , Jingguo AU - Zhang , Jinling JO - Communications in Mathematical Research VL - 2 SP - 97 EP - 109 PY - 2019 DA - 2019/11 SN - 33 DO - http://doi.org/10.13447/j.1674-5647.2017.02.01 UR - https://global-sci.org/intro/article_detail/cmr/13410.html KW - congruence, epigroup, completely 0-simple semigroup AB -

Let $\cal P$ denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any  congruence either  contains $\cal P$ or its join with $\mathcal P$ is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.

Jingguo Liu & Jinling Zhang. (2019). $\cal P$-Congruence-Free Epigroups. Communications in Mathematical Research . 33 (2). 97-109. doi:10.13447/j.1674-5647.2017.02.01
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