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When rings of differential operators are maximal orders

Published online by Cambridge University Press:  24 October 2008

M. Chamarie  and
J. T. Stafford
M. Chamarie
Affiliation:
Département de Mathematiques, Université Claude Bernard, Lyon, France
J. T. Stafford
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT
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Abstract

Let A be a commutative domain, finitely generated as an algebra over a field k of characteristic zero and write (A) for the ring of k -linear differential operators. Then A is an Ore domain with quotient division ring, say Q. Our main result is that A is a maximal order in Q if and only if (i) A = ∩{Ap: height (p) = 1} and (ii) A is geometrically unibranched. In this case A is also a Krull domain with no reflexive ideals. We also determine some conditions under which A is simple.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 3 , November 1987 , pp. 399 - 410
Copyright
Copyright © Cambridge Philosophical Society 1987

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