Concave Soft Sets, Critical Soft Points, and Union-Soft Ideals of Ordered Semigroups

الملخص EN

The notions of union-soft semigroups, union-soft l-ideals, and union-soft r-ideals are introduced, and related properties are investigated.

Characterizations of a union-soft semigroup, a union-soft l-ideal, and a union-soft r-ideal are provided.

The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-soft l-ideals and union-soft r-ideals are investigated.

Using the notions of union-soft l-ideals and union-soft r-ideals, conditions for an ordered semigroup to be regular are considered.

The concepts of concave soft sets and critical soft points are introduced, and their properties are discussed.