Mathematics / Matematik

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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; Gürbüz, Ezgi
    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.