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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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Keywords: Inertial coefficient ring, lifting idempotents, Hensel ring, separable algebra
Article copyright: © Copyright 1976 American Mathematical Society