The dimension graph of a commutative ring

被引：0
|
作者：
Babaei, S. [1 ]
Sevim, E. Sengelen [1 ]
机构：
[1] Istanbul Bilgi Univ, Fac Engn & Nat Sci, Dept Math, Istanbul, Turkiye
来源：
COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 12期
关键词：
Dimension graphs; Krull dimension-dependent ideals; strong dimension graphs;
D O I：
10.1080/00927872.2024.2362931
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper introduces a simple graph associated to a commutative ring. Nonzero ideals I and J of a commutative ring R are called Krull dimension-dependent whenever dimR/(I+J)=min{dimR/I,dimR/J} . Based on this, we introduce the dimension graph of R. We study and investigate this graph, and we determine all rings with disconnected dimension graph. Moreover, we introduce strongly Krull dimension-dependent ideals, and we examine these ideals using a subgraph of the dimension graph.
引用
收藏
页码：5005 / 5014
页数：10
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