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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A splitting theorem for algebras over commutative von Neumann regular rings


Author: William C. Brown
Journal: Proc. Amer. Math. Soc. 36 (1972), 369-374
MSC: Primary 16A16; Secondary 16A56
MathSciNet review: 0314887
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Abstract: Let R be a commutative von Neumann ring. Let A be an R-algebra which is finitely generated as an R-module and has $ A/N$ separable over R. Here N is the Jacobson radical of A. Then it is shown that there exists an R-separable subalgebra S of A such that $ S + N = A$ and $ S \cap N = 0$. Further it is shown that if T is another R-separable subalgebra of A for which $ T + N = A$ and $ T \cap N = 0$, then there exists an element $ n \in N$ such that $ (1 - n)S{(1 - n)^{ - 1}} = T$. This result is then used to determine the structure of all strong inertial coefficient rings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0314887-7
PII: S 0002-9939(1972)0314887-7
Keywords: von Neumann ring, strong inertial coefficient ring
Article copyright: © Copyright 1972 American Mathematical Society