On quasi primary ideals and weakly quasi primary ideals

‎Let R be a commutative ring with identity‎. ‎A proper ideal Q‎‎of R is called quasi primary (weakly quasi primary) if whenever ab\in Q (۰\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 avoidance‎‎theorem‎. ‎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 various‎‎examples and characterizations of quasi primary and weakly quasi primary and we investigate‎‎the relations between them‎.

کلیدواژه ها:

prime ideal‎ ، ‎quasi primary ideal‎ ، ‎weakly quasi primary ideal‎