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ASLANKARAYİĞİT UĞURLU, EMEL

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ASLANKARAYİĞİT UĞURLU

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2014 - 201932020 - 20232
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Author: TEKİR, ÜNSAL × End date: 2023 ×

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Now showing 1 - 5 of 5
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    PublicationOpen Access
    Second and Secondary Lattice Modules
    (2014) ASLANKARAYİĞİT UĞURLU, EMEL; Çallıalp, Fethi; Tekir, Ünsal; Uğurlu, Emel Aslankarayiğit; Oral, Kürşat Hakan
    Let M be a lattice module over the multiplicative lattice L . A nonzero L -lattice module M is called second if for each a ∈ L , a 1 M = 1 M or a 1 M = 0 M . A nonzero L- lattice module M is called secondary if for each a ∈ L , a 1 M = 1 M or a n 1 M = 0 M for some n > 0 . Our objective is to investigative properties of second and secondary lattice modules.
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    PublicationOpen Access
    Prime, weakly prime and almost prime elements in multiplication lattice modules
    (SCIENDO, 2016-01-01) ASLANKARAYİĞİT UĞURLU, EMEL; Ugurlu, Emel Aslankarayigit; Callialp, Fethi; Tekir, Unsal
    In this paper, we study multiplication lattice modules. We establish a new multiplication over elements of a multiplication lattice module. With this multiplication, we characterize idempotent element, prime element, weakly prime element and almost prime element in multiplication lattice modules.
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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
    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 \" 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≠0, S⊆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 \" 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∈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⊆IM⊆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 \" 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 \" 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 \" 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⋉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⋉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.
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    PublicationMetadata only
    Generalizations of 2-absorbing primary ideals of commutative rings
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2016) ASLANKARAYİĞİT UĞURLU, EMEL; Badawi, Ayman; Tekir, Unsal; Aslankarayigit Ugurlu, Emel; Ulucak, Gulsen; Yetkin Celikel, Ece
    Let R be a commutative ring with 1 not equal 0 and S(R) be the set of all ideals of R. In this paper, we extend the concept of 2-absorbing primary ideals to the context of 0-2-absorbing primary ideals. Let phi : S(R) -> S(R) U null set be a function. A proper ideal I of R is said to be a phi-2-absorbing primary ideal of R if whenever a, b, c is an element of R with abc is an element of I - phi (I) implies ab is an element of I or ac is an element of root I or be E. A number of results concerning phi-2-absorbing primary ideals are given.