Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0422333
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A32

Retrieve articles in all journals with MSC: 16A32

Additional Information

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