On quasi primary ideals and weakly quasi primary ideals

Document Type : Research Articles

Author

Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran

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∈Q (0≠ab∈Q) for some a,b∈R‎, ‎then a∈Q or b∈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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