Rings with the Beachy-Blair condition

Details Rings with the Beachy-Blair condition Rings with the Beachy-Blair condition

2010-11-02

arxiv.org/abs/1011.0656v2

Mathematics

Rings and Algebras

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Scientific paper

A ring satisfies the left Beachy-Blair condition if each of its faithful left ideal is cofaithful. Every left zip ring satisfies the left Beachy-Blair condition, but both properties are not equivalent. In this paper we will study the similarities and the differences between zip rings and rings with the Beachy-Blair condition. We will also study the relationship between the Beachy-Blair condition of a ring and its skew polynomial and skew power series extensions. We give an example of a right zip ring that is not left zip, proving that the zip property is not symmetric.

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