Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] G. V. Dorofeyev, An example of a solvable but nonnilpotent alternative ring, Uspehi Mat. Nauk 15 (1960), no. 3(93), 147-150; English transl., Amer. Math. Soc. Transl. (2) 37 (1964), 79-83. MR 0111778 (22:2639)
  • [2] E. Kleinfeld, Assosymmetric rings, Proc. Amer. Math. Soc. 8 (1957), 983-986. MR 0089833 (19:726g)
  • [3] David Rodabaugh, On the Wedderburn principal theorem, Trans. Amer. Math. Soc. 138 (1969), 343-361. MR 0330240 (48:8578)
  • [4] R. Schafer, An introduction to non associative algebras, Pure and Appl. Math., vol. 22, Academic Press, New York, 1966. MR 0210757 (35:1643)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17E05

Retrieve articles in all journals with MSC: 17E05

Additional Information

Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society