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Primitive noetherian algebras with big centers


Author: Ronald S. Irving
Journal: Proc. Amer. Math. Soc. 129 (2001), 1587-1593
MSC (2000): Primary 16D60, 16P40; Secondary 16S36
DOI: https://doi.org/10.1090/S0002-9939-00-05809-3
Published electronically: October 31, 2000
MathSciNet review: 1814084
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Abstract:

Recent work of Artin, Small, and Zhang extends Grothendieck's classical commutative algebra result on generic freeness to a large family of non-commutative algebras. Over such an algebra, any finitely-generated module becomes free after localization at a suitable central element. In this paper, a construction is given of primitive noetherian algebras, finitely generated over the integers or over algebraic closures of finite fields, such that the faithful, simple modules don't satisfy such a freeness condition. These algebras also fail to satisfy a non-commutative version of the Nullstellensatz.


References [Enhancements On Off] (What's this?)

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Additional Information

Ronald S. Irving
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: irving@math.washington.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05809-3
Keywords: Generic freeness, Nullstellensatz
Received by editor(s): September 9, 1999
Published electronically: October 31, 2000
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society

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