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Information Journal Paper

Title

On Quasi Primary Ideals and Weakly Quasi Primary Ideals

Pages

  106-117

Abstract

 Let $R$ be a commutative ring with identity‎. ‎A proper ideal $Q$‎ ‎of $R$ is called quasi primary (weakly quasi primary) if whenever $ab\in Q$ ($0\neq ab\in Q$) for some $a, b \in R$‎, ‎then $a\in \sqrt{Q}$ or $b\in \sqrt{Q}$‎. ‎In this paper‎, ‎we study quasi primary (weakly quasi primary) ideals which are generalization of prime ideals‎. ‎Our study provides an analogous to the prime avoidance‎ ‎theorem‎. ‎We determined the Noetherian rings that each ideal of them is quasi primary and the rings that each ideal of them is weakly quasi primary‎. ‎Besides giving various‎ ‎examples and characterizations of quasi primary and weakly quasi primary and we investigate‎ ‎the relations between them‎.

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