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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Filtrations in semisimple rings


Author: D. S. Passman
Journal: Trans. Amer. Math. Soc. 357 (2005), 5051-5066
MSC (2000): Primary 16W70, 16P20, 16W10
DOI: https://doi.org/10.1090/S0002-9947-05-03686-X
Published electronically: March 31, 2005
MathSciNet review: 2165397
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Abstract: In this paper, we describe the maximal bounded $\mathbb{Z} $-filtrations of Artinian semisimple rings. These turn out to be the filtrations associated to finite $\mathbb{Z} $-gradings. We also consider simple Artinian rings with involution, in characteristic $\neq 2$, and we determine those bounded $\mathbb{Z} $-filtrations that are maximal subject to being stable under the action of the involution. Finally, we briefly discuss the analogous questions for filtrations with respect to other Archimedean ordered groups.


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

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Additional Information

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: passman@math.wisc.edu

DOI: https://doi.org/10.1090/S0002-9947-05-03686-X
Received by editor(s): October 29, 2003
Received by editor(s) in revised form: March 16, 2004
Published electronically: March 31, 2005
Additional Notes: The author’s research was supported in part by NSA grant 144-LQ65. He would also like to thank Yiftach Barnea for interesting conversations on this problem.
Article copyright: © Copyright 2005 American Mathematical Society