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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inertial coefficient rings and the idempotent lifting property
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by Ellen E. Kirkman PDF
Proc. Amer. Math. Soc. 61 (1976), 217-222 Request permission

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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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