Algebras without noetherian filtrations

We provide examples of finitely generated noetherian PI algebras for which there is no finite dimensional filtration with a noetherian associated graded ring; thus we answer negatively a question of Lorenz (1988).

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2003-05, Vol.131 (5), p.1329-1338
Main Authors: Stafford, J. T., Zhang, J. J.
Format: Article
Language:English
Subjects:
Algebra
Associative rings and algebras
College mathematics
Exact sciences and technology
Filtration
Integers
Mathematical growth
Mathematical rings
Mathematical theorems
Mathematics
Sciences and techniques of general use
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Description
Summary:We provide examples of finitely generated noetherian PI algebras for which there is no finite dimensional filtration with a noetherian associated graded ring; thus we answer negatively a question of Lorenz (1988).
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-02-06972-1