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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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Noetherian down-up algebras
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by Ellen Kirkman, Ian M. Musson and D. S. Passman PDF
Proc. Amer. Math. Soc. 127 (1999), 3161-3167 Request permission

Abstract:

Down-up algebras $A= A(\alpha ,\beta ,\gamma )$ were introduced by G. Benkart and T. Roby to better understand the structure of certain posets. In this paper, we prove that $\beta \neq 0$ is equivalent to $A$ being right (or left) Noetherian, and also to $A$ being a domain. Furthermore, when this occurs, we show that $A$ is Auslander-regular and has global dimension 3.
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Additional Information
  • Ellen Kirkman
  • Affiliation: Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109
  • MR Author ID: 101920
  • Email: kirkman@mthcsc.wfu.edu
  • Ian M. Musson
  • Affiliation: Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
  • MR Author ID: 189473
  • Email: musson@csd.uwm.edu
  • D. S. Passman
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
  • MR Author ID: 136635
  • Email: passman@math.wisc.edu
  • Received by editor(s): January 28, 1998
  • Published electronically: May 4, 1999
  • Additional Notes: This research was supported in part by NSF Grants DMS-9500486 and DMS-9622566.
  • Communicated by: Lance W. Small
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3161-3167
  • MSC (1991): Primary 16E70, 16P40
  • DOI: https://doi.org/10.1090/S0002-9939-99-04926-6
  • MathSciNet review: 1610796