Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2014; 51(4): 1163-1173

Printed July 1, 2014

https://doi.org/10.4134/BKMS.2014.51.4.1163

Copyright © The Korean Mathematical Society.

On 2-absorbing primary ideals in commutative rings

Ayman Badawi, Unsal Tekir, and Ece Yetkin

American University of Sharjah, Marmara University, Marmara University

Abstract

Let $R$ be a commutative ring with $1 \not = 0$. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal $I$ of $R$ is called a 2-absorbing primary ideal of $R$ if whenever $a,b,c\in R$ and $abc\in I$, then $ab\in I$ or $ac\in \sqrt{I}$ or $bc\in \sqrt{I}$. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.

Keywords: primary ideal, prime ideal, 2-absorbing ideal, n-absorbing ideal

MSC numbers: Primary 13A15; Secondary 13F05, 13G05