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ASLANKARAYİĞİT UĞURLU, EMEL

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ASLANKARAYİĞİT UĞURLU

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EMEL

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2020 - 20236
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End date: 2023 × Start date: 2020 ×

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Now showing 1 - 6 of 6
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    PublicationOpen Access
    On quası n-ideals of commutative rings
    (2022-12-01) ASLANKARAYİĞİT UĞURLU, EMEL; Anebri A., Mahdou N., ASLANKARAYİĞİT UĞURLU E.
    Let R be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of n-ideals and the class of (2, n)-ideals. A proper ideal I of R is said to be a quasi n-ideal if root I is an n-ideal of R. Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the n-ideals, the quasi primary ideals, the (2, n)-ideals and the pr-ideals. Moreover, we use the quasi n-ideals to characterize some kind of rings. Finally, we investigate quasi n-ideals under various contexts of constructions such as direct product, power series, idealization, and amalgamation of a ring along an ideal.
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    PublicationMetadata only
    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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    PublicationOpen Access
    Pure Elements and Dual Notions of Prime Elements in Lattice Modules
    (2020-04-20) ASLANKARAYİĞİT UĞURLU, EMEL; Emel ASLANKARA YİĞİT UĞURLU
    This paper deals with the pure elements and the dual notions of prime elements(that is, second elements). For this, it introduces the definitions of second element andcoprime element. Then it is shown that the concepts of the second element and coprimeelement are equivalent. Moreover, this study gives us a characterization of comultiplicationmodules. Finally, it defines pure elements and obtains the relation among pure, idempotentand multiplication elements.
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    PublicationOpen Access
    Generalizations of r-ideals of commutative rings
    (TAYLOR & FRANCIS LTD, 2021-11-17) ASLANKARAYİĞİT UĞURLU, EMEL; Ugurlu, Emel Aslankarayigit
    In this study, we present generalizations of the concept of r-ideals in commutative rings with a nonzero identity. Let R be a commutative ring with 0 not equal 1 and L(R) be the lattice of all ideals of R. Suppose that phi:L(R) -> L(R) boolean OR {circle divide} is a function. A proper ideal I of R is called a phi-r-ideal of R if whenever ab is an element of I and Ann(a) = (0) imply that b is an element of I for each a,b is an element of R. In addition to proven many properties of phi-r-ideals, we also examine the concept of phi-r-ideals in a trivial ring extension and use them to characterize total quotient rings.
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    PublicationMetadata only
    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.
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    PublicationOpen Access
    S-principal ideal multiplication modules
    (2023-01-01) ASLANKARAYİĞİT UĞURLU, EMEL; TEKİR, ÜNSAL; Aslankarayiğit Uğurlu E., Koç S., Tekir Ü.
    In this paper, we studyS-Principal ideal multiplication modules. LetA&#x2009;\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">A A be a commutative ring with1&#x2260;0,&#x2009;S&#x2286;A\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">1≠0, S⊆A1≠0, S⊆Aa multiplicatively closed set andM&#x2009;\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">M M anA-module. A submoduleNofMis said to be anS-multipleofMif there exists&#x2208;S\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">s∈Ss∈Sand a principal idealIofAsuch thatsN&#x2286;IM&#x2286;N\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">sN⊆IM⊆NsN⊆IM⊆N.M&#x2009;\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">M M is said to be anS-principal ideal multiplication moduleif every submoduleN&#x2009;\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">N N ofM&#x2009;\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">M M is anS-multiple ofM. Various examples and properties ofS-principal ideal multiplication modules are given. We investigate the conditions under which the trivial extensionA&#x22C9;M\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">A⋉MA⋉Mis anS&#x22C9;0\" role=\"presentation\" style=\"display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\">S⋉0S⋉0-principal ideal ring. Also, we prove Cohen type theorem forS-principal ideal multiplication modules in terms ofS-prime submodules.