Generalizations of 2-absorbing primaryideals of commutative rings

Authors

AYMAN BADAWI
ÜNSAL TEKİR
EMEL ASLANKARAYİĞİT UĞURLU
GÜLŞEN ULUCAK
ECE YETKİN CELİKEL

DOI

10.3906/mat-1505-43

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

First Page

703

Last Page

717

Recommended Citation

BADAWI, AYMAN; TEKİR, ÜNSAL; UĞURLU, EMEL ASLANKARAYİĞİT; ULUCAK, GÜLŞEN; and CELİKEL, ECE YETKİN (2016) "Generalizations of 2-absorbing primaryideals of commutative rings," Turkish Journal of Mathematics: Vol. 40: No. 3, Article 20. https://doi.org/10.3906/mat-1505-43
Available at: https://journals.tubitak.gov.tr/math/vol40/iss3/20