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

Jingguo Liu & Jinling Zhang

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

  • AMS Subject Headings

20M10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liujingguo@lyu.edu.cn (Jingguo Liu)

  • BibTex
  • RIS
  • TXT
@Article{CMR-33-97, author = {Jingguo and Liu and liujingguo@lyu.edu.cn and 5449 and School of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005 and Jingguo Liu and Jinling and Zhang and and 5452 and Lanshan Education and Physical Education Bureau, Linyi, Shandong, 276005 and Jinling Zhang}, 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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