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Proceedings of the American Mathematical Society

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

 

 

Hereditary finitely generated algebras satisfying a polynomial identity


Authors: Ellen E. Kirkman and James Kuzmanovich
Journal: Proc. Amer. Math. Soc. 83 (1981), 461-466
MSC: Primary 16A14; Secondary 16A38
DOI: https://doi.org/10.1090/S0002-9939-1981-0627670-5
MathSciNet review: 627670
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Abstract: If $ \Lambda $ is a right and left p.p. ring which satisfies a polynomial identity and is a finitely generated algebra over its center, then $ \Lambda \simeq \Gamma \times \Omega $, where $ \Gamma $ is a semiprime ring having a von Neumann regular classical quotient ring which is module-finite over its center and $ \Omega $ has nonzero prime radical at each of its Pierce stalks. If $ \Lambda $ is right and left hereditary, then $ \Gamma $ is an order over a commutative hereditary ring in the sense of [7]; the ring $ \Omega $ is then a direct product of finitely many indecomposable piecewise domains.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627670-5
Article copyright: © Copyright 1981 American Mathematical Society