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N-group SI-action and its applications to N-group theory

Sezer A S, Atagün A O, Ҫaǧman N

Fasciculi Mathematici

2014

Nr 52

139--153

In this paper, we define a new concept, called N-group soft intersection action (SI) on a soft set. This new notion gathers soft set theory, set theory and N-group theory together and it shows how a soft set effects on an N-group structure in the mean of intersection and inclusion of sets. We then obtain its basic properties with illustrative examples and derive some analog of classical N-group theoretic concepts for N-group SI-actions. Finally, we give the applications of N-group SI-actions to N-group theory.

A new view to N-group theory: soft N-groups

Sezer A S, Atagün A O, Çağman N

Fasciculi Mathematici

2013

Nr 51

123--140

Molodtsov introduced the concept of soft sets. In this paper, we present the definition of soft N-groups and construct some basic properties by using N-groups and Molodtsov's definition of soft sets. We introduce the notions of soft N-subgroups, soft N-ideal, N-idealistic soft N-groups and soft N-group homomorphisms. Moreover, the relations between N-idealistic soft N-groups and soft N-groups are investigated under certain conditions of the near-ring N and these relations are illustrated by many examples.