On wsq-primary ideals - ASLANKARAYİĞİT UĞURLU, EMEL; TEKİR, ÜNSAL (My University, 2023)
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.
Keywords: Temel Bilimler; Natural Sciences; Temel Bilimler (SCI); Doğa Bilimleri Genel; ÇOK DİSİPLİNLİ BİLİMLER; Natural Sciences (SCI); NATURAL SCIENCES, GENERAL; MULTIDISCIPLINARY SCIENCES; Multidisipliner; Multidisciplinary; primary ideal; weakly primary ideal; quasi-primary ideal; weakly 2-prime ideal; strongly quasi-primary ideal