Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Gürbüz, EzgiHas files: Yes

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  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Unique decompositions into w-ideals for strong Mori domains
    (World Scientific Publishing, 2022) Hamdi, Haleh; Ay Saylam, Başak; Ay Saylam, Başak; Gürbüz, Ezgi; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    A 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, Ezgi; Ay Saylam, Başak; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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.