On 2-absorbing primary ideals in commutative rings
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1163-1173
Published online July 1, 2014
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
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