Some non-chromatic rings
作者:
S.M. Bhatwadekar,
Mahesh N. Dumaldar,
Pramod K. Sharma,
期刊:
Communications in Algebra
(Taylor Available online 1998)
卷期:
Volume 26,
issue 2
页码: 477-505
ISSN:0092-7872
年代: 1998
DOI:10.1080/00927879808826143
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
LetRbe a commutative ring with identity. ConsiderRas a simple graph with vertices elements ofRwhere any two distinct elements x, y ϵ R are adjacent if and only if xy = 0. Beck [2] conjectured that ℵ(R) =c1(R), for all colorings R. Anderson and Naseer [1] provided a counter example to the conjecture i.e., gave an example of a non-chromatic ring. This paper generalizes the example and gives a large class of non-chromatic rings [Theorem 1.1]• A detailed analysis of the graph of these rings is also provided.
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