Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 1Citation - Scopus: 1Unique decompositions into w-ideals for strong Mori domains(World Scientific Publishing, 2022) Hamdi, Haleh; Ay Saylam, Başak; Gürbüz, EzgiA commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module that decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism classes of the indecomposable ideals. In [P. Goeters and B. Olberding, Unique decomposition into ideals for Noetherian domains, J. Pure Appl. Algebra 165 (2001) 169-182], the UDI property has been characterized for Noetherian integral domains. In this paper, we aim to study the UDI-like property for strong Mori domains; domains satisfying the ascending chain condition on w-ideals.Article Unique decompositions into regular ideals for Marot rings(Taylor & Francis, 2022) Ay Saylam, Başak; Gürbüz, EzgiLet R be a commutative ring. We say that R has the unique decomposition into regular ideals (UDRI) property if, for any R-module which decomposes into a finite direct sum of regular ideals, this decomposition is unique up to the order and isomorphism class of the regular ideals. In this paper, we will prove some preliminary results for Marot rings whose regular ideals are finitely generated and give a necessary and sufficient condition for these rings to satisfy the UDRI property.Article Es-W(Taylor & Francis, 2021) Ay Saylam, Başak; Hamdi, HalehWe introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if (I-2)(w) = (JI)(w) for some t-invertible ideal J of R contained in I, and I is called weakly ES-w-stable if I-w = (JE)(w) for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.Article Citation - WoS: 2Citation - Scopus: 2Integrally Closed Rings Which Are Prufer(Taylor and Francis Ltd., 2019) Ay Saylam, BaşakLet R be a commutative ring with zero divisors. It is well known that if R is integrally closed, then R is a Prufer domain if and only if there is an integer n > 1 such that, for all . We soften this result for commutative rings with zero divisors by proving that this integer n does not have to work for all a, b is an element of R.