title: Ideal theory in semigroups based on intersectional soft sets.
abstract: The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discussed. We prove that the soft intersection of int-soft left (resp., right) ideals (resp., int-soft semigroups) is also int-soft left (resp., right) ideals (resp., int-soft semigroups). The concept of int-soft quasi-ideals is also introduced, and characterization of a regular semigroup is discussed.
authors.affiliation: Department of Mathematics, Jeju National University, Jeju 690-756, Republic of Korea.
authors.forename: Seok Zun
authors.initials: SZ
authors.lastname: Song
authors.affiliation: Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea.
authors.forename: Hee Sik
authors.identifier: 0000-0001-5321-5919
authors.initials: HS
authors.lastname: Kim
authors.affiliation: Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of Korea.
authors.forename: Young Bae
authors.initials: YB
authors.lastname: Jun
mesh_terms: D008962:Models, Theoretical