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 quasi-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 semigroup.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.
Authors: Aslıhan Sezgin
DOI: https://doi.org/10.14744/sigma.2023.00093
Publish Year: 2023
