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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Nil subsets of graded algebras


Authors: S. Montgomery and L. W. Small
Journal: Proc. Amer. Math. Soc. 126 (1998), 653-656
MSC (1991): Primary 16N40, 16W40, 16P40; Secondary 16S30
MathSciNet review: 1423323
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Abstract: We prove that if $A$ is a Noetherian $\mathbf Z$-graded algebra, then the Jacobson radical of $A$ is nilpotent under mild hypotheses on $A_0$. We also consider affine PI-algebras graded by torsion groups. Finally we prove a Nullstellensatz-type theorem for enveloping algebras of Lie color algebras.


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Additional Information

S. Montgomery
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: smontgom@math.usc.edu

L. W. Small
Affiliation: Department of Mathematics, University of California, La Jolla, California 92093
Email: lwsmall@uscd.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04131-8
Received by editor(s): June 17, 1996
Received by editor(s) in revised form: August 23, 1996
Additional Notes: Both authors were supported by the NSF
Communicated by: Ken Goodearl
Article copyright: © Copyright 1998 American Mathematical Society