Soft groups and normalistic soft groups

Soft Inverse Semigroup

“…Aktas H, et al give the concept soft group. [2], Ali discusses soft binary relationon and soft equivalence on set [3], Sezgin A, Atagün A O gives the concept normalistic soft group [4] . In this paper, based on soft sets, soft inverse semigroup and soft congruence on inverse semigroup are syudied.…”

“…4 Let S is an inverse semigroup, G is a group, : f S G is semigroup morphism,and G is the maximum group morphic image of S, if A is soft group congruence on S, then ( ( ),A f ) is soft group congruence on G. Soft quotient soft…”

A new view to ring theory via soft union rings, ideals and bi-ideals

“…The soft set theory provides a natural frame-work for generalizing several basic notions of algebra such as groups [2,3], semirings [4], rings [5], BCK/BCI-algebras [6][7][8], BL-algebras [9], near-rings [10] and soft substructures and union soft substructures [11,12].…”

Some new operations of soft sets

“…Aktas et al [11] gave a definition of soft groups and derived their basic properties. Sezgin et al [12] corrected some of the problematic cases in a previous paper by Aktas and Cagman, and introduced the concept of normalistic soft groups and the homomorphism of normalistic soft groups, studied their several related properties, and investigated some structures that are preserved under normalistic soft group homomorphisms. Atagün et al [13] introduced soft subrings and soft ideals of a ring, soft subfields of a field and soft submodule of a left R-module, and studied some related properties.…”