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A characterization of semilocal inertial coefficient rings


Authors: W. C. Brown and E. C. Ingraham
Journal: Proc. Amer. Math. Soc. 26 (1970), 10-14
MSC: Primary 13.95
DOI: https://doi.org/10.1090/S0002-9939-1970-0260730-2
MathSciNet review: 0260730
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Abstract: A commutative ring $ R$ with identity is called an inertial coefficient ring if every finitely generated $ R$-algebra $ A$ with $ A/N$ separable over $ R$ contains a separable subalgebra $ S$ such that $ S + N = A$, where $ N$ is the Jacobson radical of $ A$. Thus inertial coefficient rings are those commutative rings $ R$ for which a generalization of the Wedderburn Principal Theorem holds for suitable $ R$-algebras. Our purpose is to prove that a commutative ring with only finitely many maximal ideals is an inertial coefficient ring (if and) only if it is a finite direct sum of Hensel rings.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0260730-2
Keywords: Inertial coefficient ring, Hensel ring, inertial subalgebra, separable algebra, lifting idempotents
Article copyright: © Copyright 1970 American Mathematical Society

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