Geodesic
On wsq-primary ideals
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 415-429

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We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $Q$ a proper ideal of $R$. The proper ideal $Q$ is said to be a weakly strongly quasi-primary ideal if whenever $0\neq ab\in Q$ for some $a,b\in R$, then $a^{2}\in Q$ or $b\in \sqrt {Q}.$ Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.
DOI : 10.21136/CMJ.2023.0259-21
Classification : 05C25, 13A15, 13A99, 13F30
Keywords: primary ideal; weakly primary ideal; quasi-primary ideal; weakly 2-prime ideal; strongly quasi-primary ideal 
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Aslankarayiğit Uğurlu, Emel; Bouba, El Mehdi; Tekir, Ünsal; Koç, Suat. On wsq-primary ideals. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 415-429. doi: 10.21136/CMJ.2023.0259-21

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