ISSN: 1304-7191 | E-ISSN: 1304-7205
Completely weakly, quasi-regular semigroups characterized by soft union Quasi ideals, (generalized) bi-ideals and semiprime ideals
1Department of Mathematics and Science Education, Amasya University, Amasya, 05100, Türkiye
Sigma J Eng Nat Sci 2023; 41(4): 868-874 DOI: 10.14744/sigma.2023.00093
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Abstract

In this paper, certain kinds of regularities of semigroups are studied by correlating soft set theory. Completely, weakly and quasi-regular semigroups are characterized by soft union qua-si-ideals, soft union (generalized) bi-ideals and soft union semiprime ideals of a semigroup. It is proved that if every soft union quasi-ideal of a semigroup is soft union semiprime, then every quasi-ideal of a semigroup is semiprime and thus, if every quasi-ideal of a semigroup is semiprime, then the semigroup is completely regular. Also, it is obtained that the case when every soft union quasi-ideal (bi-ideal, generalized bi-ideal, respectively) of a semigroup is soft union semiprime is equivalent to the case when every quasi-ideal (bi-ideal, generalized bi-ideal, respectively) of a semigorup is semiprime, where the semigroup is completely semi-group. Similar characterizations are obtained for weakly and quasi-regular semigroups. By these characterizations, we intent to bring a new perspective to the regularities of semigroup theory via soft set theory. Further study can be focused on soft union tri quasi-ideals, soft union bi-quasi ideals, soft union lateral bi-quasi-ideals and soft union lateral tri-quasi ideals of a semigroup.