McCoy rings and zero-divisors

Victor Camillo; Pace P Nielsen

doi:10.1016/j.jpaa.2007.06.010

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McCoy rings and zero-divisors

Victor Camillo and Pace P Nielsen

Journal of pure and applied algebra, Vol.212(3), pp.599-615

2008

DOI: 10.1016/j.jpaa.2007.06.010

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Abstract

We investigate relations between the McCoy property and other standard ring theoretic properties. For example, we prove that the McCoy property does not pass to power series rings. We also classify how the McCoy property behaves under direct products and direct sums. We prove that McCoy rings with 1 are Dedekind finite, but not necessarily Abelian. In the other direction, we prove that duo rings, and many semi-commutative rings, are McCoy. Degree variations are defined, studied, and classified. The McCoy property is shown to behave poorly with respect to Morita equivalence and (infinite) matrix constructions.

Details

Title: Subtitle: McCoy rings and zero-divisors
Creators: Victor Camillo
Pace P Nielsen
Resource Type: Journal article
Publication Details: Journal of pure and applied algebra, Vol.212(3), pp.599-615
DOI: 10.1016/j.jpaa.2007.06.010
ISSN: 0022-4049
eISSN: 1873-1376
Language: English
Date published: 2008
Academic Unit: Mathematics
Record Identifier: 9983985877502771

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