Czechoslovak Mathematical Journal, Vol. 73, No. 2, pp. 415-429, 2023
On wsq-primary ideals
Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç
Received July 23, 2021. Published online January 3, 2023.
Abstract: 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.
Affiliations: Emel Aslankarayiğit Uğurlu, Department of Mathematics, Marmara University, GMK boulevard No:17, 34722 Istanbul, Turkey, e-mail: emel.aslankarayigit@marmara.edu.tr; El Mehdi Bouba, Mathematics Department, Pluridisciplinary Faculty, Mohammed First University, B.P. 300, Selouane, Nador 62700, Morocco, e-mail: mehdi8bouba@hotmail.fr; Ünsal Tekir, Department of Mathematics, Marmara University, GMK boulevard No:17, 34722 Istanbul, Turkey, e-mail: utekir@marmara.edu.tr; Suat Koç (corresponding author), Department of Mathematics, Istanbul Medeniyet University, D100 Highway No:98, Istanbul, Turkey, e-mail: suat.koc@medeniyet.edu.tr
