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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Solvable assosymmetric rings are nilpotent


Authors: David Pokrass and David Rodabaugh
Journal: Proc. Amer. Math. Soc. 64 (1977), 30-34
MSC: Primary 17E05
MathSciNet review: 0463255
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Abstract: Assosymmetric rings are ones which satisfy the law $ (x,y,z) = (P(x),P(y),P(z))$ for each permutation P of x, y, z. Let A be an assosymmetric ring having characteristic different from 2 or 3. We show that if A is solvable then A is nilpotent. Also, if each subring generated by a single element is nilpotent, and if A has D.C.C. on right ideals, then A is nilpotent. We also give an example showing that the Wedderburn Principal Theorem fails for assosymmetirc rings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0463255-0
PII: S 0002-9939(1977)0463255-0
Article copyright: © Copyright 1977 American Mathematical Society