Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

Browse

Filters

2020 - 20223

Settings

Start date: 2020Institution Author: search.filters.institutionAuthor.Ay Saylam, Başak

Search Results

Now showing 1 - 3 of 3
  • Article
    Unique decompositions into regular ideals for Marot rings
    (Taylor & Francis, 2022) Ay Saylam, Başak; Gürbüz, Ezgi
    Let 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, Haleh
    We 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: 1
    Citation - Scopus: 1
    Stability in Commutative Rings
    (TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2020) Ay Saylam, Başak
    Let R be a commutative ring with zero-divisors and I an ideal of R. I is said to be ES-stable if JI = $I^2$ for some invertible ideal J ? I , and I is said to be a weakly ES-stable ideal if there is an invertible fractional ideal J and an idempotent fractional ideal E of R such that I = JE . We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?