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)

 

 

Rings having solvable adjoint groups


Authors: P. B. Bhattacharya and S. K. Jain
Journal: Proc. Amer. Math. Soc. 25 (1970), 563-565
MSC: Primary 16.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0271154-6
MathSciNet review: 0271154
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ ^\circ R$ denote the group of quasi-regular elements of a ring $ R$ with respect to circle operation. The following results have been proved: (1) If $ R$ is a perfect ring and $ ^\circ R$ is finitely generated solvable group then $ R$ is finite and hence $ ^\circ R = {P_1} \circ {P_2} \circ \; \cdots \; \circ {P_m}$ where $ {P_i}$ are pairwise commuting $ p$-groups. (2) Let $ R$ be a locally matrix ring or a prime ring with nonzero socle. Then $ \circ R$ is solvable iff $ R$ is either a field or a $ 2 \times 2$ matrix ring over a field having at most $ 3$ elements.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16.50

Retrieve articles in all journals with MSC: 16.50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0271154-6
Keywords: Perfect rings, locally matrix rings, prime rings with nonzero socles, solvable adjoint groups
Article copyright: © Copyright 1970 American Mathematical Society