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Link between a natural centralizer and the smallest essential ideal in structural matrix rings

 

作者: Leon Van wyk,  

 

期刊: Communications in Algebra  （Taylor Available online 1999）
卷期: Volume 27, issue 8  

页码: 3675-3683

 

ISSN:0092-7872

 

年代: 1999

 

DOI:10.1080/00927879908826655

 

出版商: Gordon and Breach Science Publishers Ltd.

 

关键词: Structural matrix ring;centralizer;esential ideal;Primary 16S50;Primary 16D25

 

数据来源: Taylor

 

摘要:

In a structural matrix ringMn(ρR) over an arbitrary ringRwe determine the centralizer of the set of matrix units inMn(ρR) associated with the anti-symmetric part of the reflexive and transitive binary relation ρ on {1,2,…,n}. If the underlying ringRhas no proper essential ideal, for example ifRis a field, then we show that the largest ideal ofMn(ρR) contained in the mentioned centralizer coincides with the smallest essential ideal ofMn(ρR).

 

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