## 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.## References

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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