Generalizations of 2-absorbing primaryideals of commutative rings

Authors : Ayman Badawi, Ünsal Tekir, Emel Aslankarayiğit Uğurlu, Gülşen Ulucak, Ece Yetkin Celikel

Pages : 703-717

View : 14 | Download : 13

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :ideals of $R$. In this paper, we extend the concept of 2-absorbing primary ideals to the context of $\phi $-2-absorbing primary ideals. Let $\phi :S(R)\rightarrow S(R)\cup \emptyset $ be a function. A proper ideal $I$ of $% R $ is said to be a $\phi $-2-absorbing primary ideal of $R$ if whenever $% a,b,c\in R$ with $abc\in I-\phi (I)$ implies $ab\in I$ or $ac\in \sqrt{I}$ or $bc\in \sqrt{I}$. A number of results concerning $\phi $-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, $phi $-prime ideal, $phi $-2-primary ideal, $phi $-2-absorbing ideal