Abstract
In this paper, we define a new type of M(G)-group action , called M(G)-group soft union(SU) action and M(G)-ideal soft union(SU) action on a soft set. This new concept illustrates how a soft set effects on an M(G)-group in the mean of union and inclusion of sets and its function as bridge among soft set theory, set theory and M(G)-group theory. We also obtain some analog of classical M(G)- group theoretic concepts for M(G)-group SU-action. Finally, we give the application of SU-actions on M(G)-group to M(G)-group theory.
Highlights
Soft set theory as in [1, 2, 11, 14, 15, 16, 18, 25, 28] was introduced in 1999 by Molodtsov [22]for dealing with uncertainties and it has gone through remarkably rapid strides in the mean of algebraic structures
Maji et al [19] presented some definitions on soft sets and based on the analysis of several operations on soft sets Ali et al [3] introduced several operations Atagun and Sezgin [4] defined the concepts of soft sub rings and ideals of a ring, soft subfields of a field and soft sub modules of a module and studied their related properties with respect to soft set operations
SU-action gathers soft set theory and set theory and M(G) –group theory, it is useful in improving the soft set theory with respect to M(G)- group structures
Summary
Soft set theory as in [1, 2, 11, 14, 15, 16, 18, 25, 28] was introduced in 1999 by Molodtsov [22]. SU-action gathers soft set theory and set theory and M(G) –group theory, it is useful in improving the soft set theory with respect to M(G)- group structures Based on this new notion, we introduce the concepts of M(G)-ideal SU-action and show that if M(G)-group SU-action over U. We investigate these notions with respect to soft image, soft pre-image and give their applications to M(G)- group theory. We first define M(G)-group soft union action, abbreviated as M(G)-group SUaction with illustrative examples We study their basic results with respect to soft set operation. 3.1Definition: Let S be an M(G)- group and be a fuzzy soft set over U, is called fuzzy SU-action on M(G)- group over U if it satisfies the following conditions;. *, one can show that the soft set is a M(G)-group SU-action over U
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