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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Commutativity of rings with abelian or solvable units


Authors: W. K. Nicholson and H. J. Springer
Journal: Proc. Amer. Math. Soc. 56 (1976), 59-62
DOI: https://doi.org/10.1090/S0002-9939-1976-0399180-2
MathSciNet review: 0399180
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Abstract | References | Additional Information

Abstract: A ring is called left suitable if idempotents can be lifted modulo every left ideal. These rings include all regular and all semiperfect rings. A left suitable ring with abelian group of units is commutative if it is either semiprime or $ 2$-torsion-free. A left suitable ring with zero Jacobson radical and solvable group of units is commutative if it is $ 6$-torsion-free.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399180-2
Keywords: Group of units, commutativity, regular rings, semiperfect rings, lifting idempotents
Article copyright: © Copyright 1976 American Mathematical Society

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