Volume 29, Issue 2
Some Characterizations of Strongly Semisimple Ordered Semigroups

Commun. Math. Res., 29 (2013), pp. 155-166.

Published online: 2021-05

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• Abstract

In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup $S$ is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of $S$. In particular, we prove that $S$ is strongly semisimple if and only if each fuzzy left ideal of $S$ is the intersection of all quasi-prime fuzzy left ideals of $S$ containing it.

• Keywords

ordered semigroup, ordered fuzzy point, quasi-prime fuzzy left ideal, strongly semisimple ordered semigroup.

20M10, 06F05

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@Article{CMR-29-155, author = {Tang , Jian and Xie , Xiangyun}, title = {Some Characterizations of Strongly Semisimple Ordered Semigroups}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {2}, pages = {155--166}, abstract = {

In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup $S$ is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of $S$. In particular, we prove that $S$ is strongly semisimple if and only if each fuzzy left ideal of $S$ is the intersection of all quasi-prime fuzzy left ideals of $S$ containing it.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19019.html} }
TY - JOUR T1 - Some Characterizations of Strongly Semisimple Ordered Semigroups AU - Tang , Jian AU - Xie , Xiangyun JO - Communications in Mathematical Research VL - 2 SP - 155 EP - 166 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19019.html KW - ordered semigroup, ordered fuzzy point, quasi-prime fuzzy left ideal, strongly semisimple ordered semigroup. AB -

In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup $S$ is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of $S$. In particular, we prove that $S$ is strongly semisimple if and only if each fuzzy left ideal of $S$ is the intersection of all quasi-prime fuzzy left ideals of $S$ containing it.

Jian Tang & Xiangyun Xie. (2021). Some Characterizations of Strongly Semisimple Ordered Semigroups. Communications in Mathematical Research . 29 (2). 155-166. doi:
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