The Krull dimension-dependent elements of a Noetherian commutative ring
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Krull Dimension-Dependent Elements, Closed Under The Krull Dimension, Associated Prime İdeals
Kaynak
Journal of Algebra and Its Applications
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
23
Sayı
2
