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.
Alehafttan, A. (2024). On quasi primary ideals and weakly quasi primary ideals. Caspian Journal of Mathematical Sciences, 13(1), 106-117. doi: 10.22080/cjms.2024.26781.1684
MLA
Alireza Alehafttan. "On quasi primary ideals and weakly quasi primary ideals". Caspian Journal of Mathematical Sciences, 13, 1, 2024, 106-117. doi: 10.22080/cjms.2024.26781.1684
HARVARD
Alehafttan, A. (2024). 'On quasi primary ideals and weakly quasi primary ideals', Caspian Journal of Mathematical Sciences, 13(1), pp. 106-117. doi: 10.22080/cjms.2024.26781.1684
VANCOUVER
Alehafttan, A. On quasi primary ideals and weakly quasi primary ideals. Caspian Journal of Mathematical Sciences, 2024; 13(1): 106-117. doi: 10.22080/cjms.2024.26781.1684
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