IJPAM: Volume 109, No. 4 (2016)

ON GRADED 2-ABSORBING PRIMARY SUBMODULES

Ece Yetkin Celikel
Department of Mathematics
Faculty of Art and Science
Gaziantep University
Gaziantep, TURKEY

Abstract. In this paper, we introduce and study the concept of graded $2$-absorbing primary submodules of graded modules over graded commutative rings generalizing graded $2$-absorbing submodules. Let $R~$be a graded ring and $% M $ be a graded $R$-module. A proper graded submodule $N$ of $M$ is called a graded 2-absorbing primary submodule of $M$ if whenever $a,b\in h(R) $ and $m\in h(M)$ and $abm\in N$, then $am\in M$- $\mathrm{Gr}(N)$ or $% bm\in M $- $\mathrm{Gr}(N)$ or $ab\in (N:_{R}M)$.

Received: July 18, 2016

Revised: August 25, 2016

Published: October 9, 2016

AMS Subject Classification: 13A02

Key Words and Phrases: graded 2-absorbing ideal, graded 2-absorbing primary ideal, graded 2-absorbing submodule, graded $2$-absorbing primary submodule
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DOI: 10.12732/ijpam.v109i4.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 869 - 879


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