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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

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Solvable subgroups in prime rings
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by Charles Lanski PDF
Proc. Amer. Math. Soc. 82 (1981), 533-537 Request permission

Abstract:

Let $R$ be a prime ring with center $Z$ and group of units $U$. The main theorem shows that any solvable normal subgroups of $U$ must lie in $Z$, provided that $R$ is not a domain, $Z$ is large enough, and that the $Z$-subalgebra generated by $U$ contains a nonzero ideal of $R$. One consequence is the determination of the structure of $R$ when $R$ has an involution and the subgroup of $U$ generated by the symmetric units is solvable.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 82 (1981), 533-537
  • MSC: Primary 16A25
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0614873-9
  • MathSciNet review: 614873