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Proceedings of the American Mathematical Society

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Krull dimension of modules
over involution rings. II


Authors: K. I. Beidar, E. R. Puczylowski and P. F. Smith
Journal: Proc. Amer. Math. Soc. 125 (1997), 355-361
MSC (1991): Primary 16W10, 16P60
DOI: https://doi.org/10.1090/S0002-9939-97-03724-6
MathSciNet review: 1371115
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $R$ be a ring with involution and invertible 2, and let $\bar S$ be the subring of $R$ generated by the symmetric elements in $R$. The following questions of Lanski are answered positively:

(i)
Must $\bar S$ have Krull dimension when $R$ does?
(ii)
Is every Artinian $R$-module Artinian as an $\bar S$-module?


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Additional Information

K. I. Beidar
Affiliation: Department of Mathematics, Moscow State University, Moscow, Russia
Address at time of publication: National Cheng–Kung University, Department of Mathematics, Tainan, Taiwan
Email: t14270@sparc1.cc.ncku.edu.tw

E. R. Puczylowski
Affiliation: Institute of Mathematics, University of Warsaw, Warsaw, Poland
Email: edmundp@mimuw.edu.pl

P. F. Smith
Affiliation: Department of Mathematics, University of Glasgow, Glasgow, Scotland
Email: pfs@maths.gla.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-97-03724-6
Received by editor(s): August 23, 1995
Additional Notes: The research of the second author was partially supported by KBN grant 2 P301 035 06.
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society