Yazar "Babaei, S." seçeneğine göre listele

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    On the compressed essential graph of a module over a commutative ring
    (World Scientific Publ Co Pte Ltd, 2021) Payrovi, S. H.; Babaei, S.; Sengelen Sevim, E.
    Let R be a commutative ring and M be an R-module. The compressed essential graph of M, denoted by EG(M) is a simple undirected graph associated to M whose vertices are classes of torsion elements of M and two distinct classes [m] and [m '] are adjacent if and only if Ann(R)(m) + Ann(R)(m ') is an essential ideal of R. In this paper, we study diameter and girth of EG(M) and we characterize all modules for which the compressed essential graph is connected. Moreover, it is proved that omega(EG(M)) = |Ass(R)(M)|, whenever R is Noetherian and M is a finitely generated multiplication module with r(Ann(R)(M)) = 0.
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    The extended graph of a module over a commutative ring
    (World Scientific Publ Co Pte Ltd, 2023) Babaei, S.; Sengelen Sevim, E.
    In this paper, we associate a simple graph to a module over a commutative ring and call it extended graph, that adjacent condition depends on the properties of annihilator submodules. We determine the structure of modules, when the associated graph is star or complete. Moreover, we look for relationships between the extended graph and the zero-divisor graph of modules.
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    The Krull dimension-dependent elements of a Noetherian commutative ring
    (World Scientific Publ Co Pte Ltd, 2024) Babaei, S.; Sevim, E. Sengelen
    In this paper, we introduce the Krull dimension-dependent elements of a Noetherian commutative ring. Let x, y be non-unit elements of a commutative ring R. x, y are called Krull dimension-dependent elements, whenever dim R/(Rx + Ry) = min{dim R/Rx, dim R/Ry}. We investigate the elements of a ring according to this property. Among the many results, we characterize the rings that all elements of them are Krull dimension-dependent and we call them, closed under the Krull dimension. Moreover, we determine the structure of the rings with Krull dimension at most 1. that are closed under the Krull dimension.