Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

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Filtrations in semisimple rings
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by D. S. Passman
Trans. Amer. Math. Soc. 357 (2005), 5051-5066
DOI: https://doi.org/10.1090/S0002-9947-05-03686-X
Published electronically: March 31, 2005
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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.
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Bibliographic Information
  • D. S. Passman
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 136635
  • Email: passman@math.wisc.edu
  • 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.
  • © Copyright 2005 American Mathematical Society
  • 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
  • MathSciNet review: 2165397