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Semigroups and rings whose zero products commute

 

作者: D.D. Anderson,   Victor Camillo,  

 

期刊: Communications in Algebra  （Taylor Available online 1999）
卷期: Volume 27, issue 6  

页码: 2847-2852

 

ISSN:0092-7872

 

年代: 1999

 

DOI:10.1080/00927879908826596

 

出版商: Gordon and Breach Science Publishers Ltd.

 

关键词: Zero divisors;16U80;20M99

 

数据来源: Taylor

 

摘要:

LetSbe a semigroup with zero 0 and letn≥ 2. We say that S satisfiesfor each permutation σ ∈SnA ringRsatisfies ZCnif (.R, .) satisfies ZCn. We show that if S satisfies ZCnfor a fixed n ≥ 3, thenSalso satisfies ZCn+1, but we give an example of a ringRwith identity which satisfies ZC2but does not satisfy ZC3We show that a semigroup with no nonzero nilpotents satisfiesZCnfor alln≥ 2 and investigate rings that satisfy ZCn.

 

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