On Graded 2-Absorbing Quasi Primary Ideals

Üregen R. N. , Tekir Ü., Shum K. P. , Koç S.

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, vol.43, no.4, pp.601-613, 2019 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 4
  • Publication Date: 2019
  • Journal Name: SOUTHEAST ASIAN BULLETIN OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index
  • Page Numbers: pp.601-613
  • Keywords: Graded 2-absorbing ideal, Graded 2-absorbing quasi primary ideal, Graded prime ideal, Graded primary ideal, Idealization of graded module

Abstract

In this article, we introduce the concept of graded 2-absorbing quasi primary ideal which is a generalization of graded prime ideal. In the first part of the paper, we give many characterizations of these classes of ideals. In the second part, we study idealization of graded modules. In particular, we investigate graded radical in the idealization of a graded module. Furthermore, we determine h-dimension of idealization of a graded module and study some classical graded ideals such as graded maximal, graded prime, graded primary, graded 2-absorbing and graded 2-absorbing quasi primary ideals.