Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Solvable assosymmetric rings are nilpotent
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17E05
  • Retrieve articles in all journals with MSC: 17E05
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