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ASLANKARAYİĞİT UĞURLU, EMEL

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ASLANKARAYİĞİT UĞURLU

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2022 - 20232
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    On wsq-primary ideals
    (2023-01-01) ASLANKARAYİĞİT UĞURLU, EMEL; TEKİR, ÜNSAL; Aslankarayiğit Uğurlu E., Tekir Ü., Koç S.
    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.
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    On 2-absorbing submodule elements in le-modules and its generalizations
    (2022-01-01) ASLANKARAYİĞİT UĞURLU, EMEL; ASLANKARAYİĞİT UĞURLU E.
    In this paper, we introduce the concept of 2-absorbing submodule elements in an le-module M as follows: a proper submodule element q in M is said to be 2-absorbing for any r,s is an element of R and m is an element of M if rsm <= q, then either rs is an element of (q : e) or rm <= q or sm <= q. Moreover, we define some generalizations of the new concept such as weakly 2-absorbing, n-absorbing, weakly n-absorbing, (n,k)-absorbing, weakly (n,k)-absorbing submodule elements in le-modules. After presenting a main example for le-modules, we study some counter examples for the generalizations. In addition to giving some characterizations for the new concepts, we investigate the relationship between prime (primary) submodule elements and them.