The Krull dimension-dependent elements of a Noetherian commutative ring
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Date
2024
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific Publ Co Pte Ltd
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
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.
Description
Keywords
Krull Dimension-Dependent Elements, Closed Under The Krull Dimension, Associated Prime İdeals
Journal or Series
Journal of Algebra and Its Applications
WoS Q Value
Q3
Scopus Q Value
Q2
Volume
23
Issue
2
