Solvable assosymmetric rings are nilpotent
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- by David Pokrass and David Rodabaugh PDF
- Proc. Amer. Math. Soc. 64 (1977), 30-34 Request permission
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.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 30-34
- MSC: Primary 17E05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0463255-0
- MathSciNet review: 0463255