On completely 2-absorbing ideals of N-groups

Abstract

We introduce the notion of completely 2-absorbing (denoted by, c-2-absorbing) ideal of an N-group G, as a generalization of completely prime ideal of module over a right near-ring N. We obtain that, for an ideal I of a monogenic N-group G, if (I: G) is a c-2-absorbing ideal of N, then I is a c-2-absorbing ideal of G. The converse also holds only when G is locally monogenic over a distributive near-ring N. We discuss the properties such as homomorphic images, inverse images of c-2-absorbing ideals of G. Examples of c-2-absorbing ideals of N-groups are given where N is non-commutative and in the sequel some results of 2-absorbing ideals from module over rings are generalized to N-groups.

Subject Classification: (2010):

• Primary 16Y30

Keywords:

• Near-ring
• Completely prime ideal
• IFP
• monogenic
• N-group