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Proceedings of the American Mathematical Society

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

 

 

Inertial coefficient rings and the idempotent lifting property


Author: Ellen E. Kirkman
Journal: Proc. Amer. Math. Soc. 61 (1976), 217-222
MSC: Primary 16A32
DOI: https://doi.org/10.1090/S0002-9939-1976-0422333-1
MathSciNet review: 0422333
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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 $ R$-subalgebra $ S$ of $ A$ such that $ A = S + N$, where $ N$ is the Jacobson radical of $ A$. We say $ A$ has the idempotent lifting property if every idempotent in $ A/N$ is the image of an idempotent in $ A$. Our main theorem is that any finitely generated algebra over an inertial coefficient ring has the idempotent lifting property.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0422333-1
Keywords: Inertial coefficient ring, lifting idempotents, Hensel ring, separable algebra
Article copyright: © Copyright 1976 American Mathematical Society