Noetherian down-up algebras

Authors:
Ellen Kirkman, Ian M. Musson and D. S. Passman

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

Published electronically:
May 4, 1999

MathSciNet review:
1610796

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Abstract | References | Similar Articles | Additional Information

Abstract: Down-up algebras were introduced by G. Benkart and T. Roby to better understand the structure of certain posets. In this paper, we prove that is equivalent to being right (or left) Noetherian, and also to being a domain. Furthermore, when this occurs, we show that 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

Email:
kirkman@mthcsc.wfu.edu

**Ian M. Musson**

Affiliation:
Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201

Email:
musson@csd.uwm.edu

**D. S. Passman**

Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706

Email:
passman@math.wisc.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04926-6

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

Article copyright:
© Copyright 1999
American Mathematical Society