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Deformations of rings

Published online by Cambridge University Press:  17 April 2009

Joe Yanik
Joe Yanik
Affiliation:
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, VA 23284, United States of America
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Abstract

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Let A and A0 be rings with a surjective homomorphism A → A0. Given a flat extension B0 of A0, a deformation of B0/A0 over A is a flat extension B of A such that B ⊗AA0 is isomorphic to B0. We show that such a deformation will exist if A0 is an Artin local ring, A is noetherian, and the homological dimension of B0 over A0 is ≤ 2. We also show that a deformation will exist if the kernel of A is nilpotent and if A0 is a finitely generted A0-algebra whose defining ideal is a local complete intersection.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 361 - 367
Copyright
Copyright © Australian Mathematical Society 1989

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