Geodesic
Generalization of 2-absorbing quasi primary ideals
Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1.

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In this article, we introduce and study the concept of $\phi$-2-absorbing quasi primary ideals in commutative rings. Let $R\ $be a commutative ring with a nonzero identity and $L(R)$ be the lattice of all ideals of $R.\ $Suppose that $\phi:L(R)\rightarrow L(R)\cup\left\{ \emptyset\right\} $ is a function. A proper ideal $I\ $of $R\ $is called a $\phi$-2-absorbing quasi primary ideal of $R\ $if $a,b,c\in R$ and whenever $abc\in I-\phi(I),$ then either $ab\in\sqrt{I}\ $or $ac\in\sqrt{I}\ $or $bc\in\sqrt{I}.\ $In addition to giving many properties of $\phi$-2-absorbing quasi primary ideals, we also use them to characterize von Neumann regular rings.
Publié le :
DOI : 10.30755/NSJOM.11842
Classification : 13A15, 16E50
Keywords: weakly 2-absorbing quasi primary ideal, $\phi$-2-absorbing quasi primary ideal, von Neumann regular ring 
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     title = {Generalization of 2-absorbing quasi primary ideals},
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Emel Aslankarayiğit Uğurlu; Suat Koç; Ünsal Tekir. Generalization of 2-absorbing quasi primary ideals. Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1. doi : 10.30755/NSJOM.11842. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.11842/

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