Journal of the
Korean Mathematical Society JKMS

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

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

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