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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: May 4, 1999
MathSciNet review: 1610796
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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
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: http://dx.doi.org/10.1090/S0002-9939-99-04926-6
PII: S 0002-9939(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