关于合并代数的最大(理想)图

IF 1 Q1 MATHEMATICS

Discrete Mathematics Letters Pub Date : 2022-10-05 DOI:10.47443/dml.2022.095

Zinat Rastgar, K. Khashyarmanesh, M. Afkhami

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引用次数: 1

摘要

设f:A→ B是具有恒等式的交换环a和B的环同态。设J是B的理想。A与B沿J相对于f的并合是由A（cid:46）（cid:47）fJ:={（A，f（A）+J）|A∈A，J∈J}给出的A×B的子环。本文研究了合并代数A（cid:46）（cid:47）fJ的共极大理想图和共极大图。特别地，我们确定了A（cid:46）（cid:47）fJ的Jacobson自由基，刻画了A（acid:46）[cid:47]fJ的最大理想图的直径，并研究了该图的团数和色数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Comaximal (Ideal) Graph Associated With Amalgamated Algebra

Let f : A → B be a ring homomorphism of the commutative rings A and B with identities. Let J be an ideal of B . The amalgamation of A with B along J with respect to f is a subring of A × B given by A (cid:46)(cid:47) f J := { ( a, f ( a )+ j ) | a ∈ A , j ∈ J } . In this paper, we investigate the comaximal ideal graph and the comaximal graph of the amalgamated algebra A (cid:46)(cid:47) f J . In particular, we determine the Jacobson radical of A (cid:46)(cid:47) f J , characterize the diameter of the comaximal ideal graph of A (cid:46)(cid:47) f J , and investigate the clique number as well as the chromatic number of this graph.

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来源期刊

Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

12 weeks