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)

 

 

Global dimension of differential operator rings


Author: K. R. Goodearl
Journal: Proc. Amer. Math. Soc. 45 (1974), 315-322
MSC: Primary 16A72
DOI: https://doi.org/10.1090/S0002-9939-1974-0382358-X
MathSciNet review: 0382358
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with finding the global homological dimension of the ring of differential operators $ R[\theta ]$ over a differential ring $ R$ with a single derivation. Examples are constructed to show that $ R[\theta ]$ may have finite dimension even when $ R$ has infinite dimension. For a commutative noetherian differential algebra $ R$ over the rationals, with finite global dimension $ n$, it is shown that the global dimension of $ R[\theta ]$ is the supremum of $ n$ and one plus the projective dimensions of the modules $ R/P$, where $ P$ ranges over all prime differential ideals of $ R$. One application derives the global dimension of the Weyl algebra over a commutative noetherian ring $ S$ of finite global dimension, where $ S$ either is an algebra over the rationals or else has positive characteristic.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A72

Retrieve articles in all journals with MSC: 16A72


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0382358-X
Keywords: Global dimension, rings of linear differential operators, differential algebra, Weyl algebras
Article copyright: © Copyright 1974 American Mathematical Society