Global Dimension of Algebra of Differential Operators

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Authors

  • A. V. Chiplunkar
     Department of Mathematics, University of Poona, Poona”7 ,IN

Abstract

Let S be a commutative ring with identity and let Ts be an S-module of derivations of S. Let Vs be the algebra of differential operators of S with respect to Ts as defined in [5]. The object of this paper is to calculate the global dimension of Vs when S and Ts are resticted suitably.

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Published

1974-12-01

How to Cite

Chiplunkar, A. V. (1974). Global Dimension of Algebra of Differential Operators. The Journal of the Indian Mathematical Society, 38(1-4), 1–17. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/16677

Issue

Volume 38, Issue 1-4, March-December 1974

Section

Articles

License

Copyright (c) 1974 A. V. Chiplunkar

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

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N. S. GOPALAKRISHNAN, On some filtered rings, Proc. bid. Acad. Sci. 56(1962), p. 148-154.

N. S. GOPALAKRISHNAN, AND R. SRIDHARAN, Homological dimension of Ore extensions, Pacific Jr. Math. 19(1966) p. 67-75.

G. HOCHSCHILD, B. KOSTANT, A. ROSENBERG, Differential forms on regular affine algebras, Trans. Am. Math. Soc. 102 (1962) p. 383-408.

I. KAPLANSKY, Commutative Rings. Lecture Notes. Queen Mary College, London.

O. ORE, Theory of non-commutative polynomials, Ann. of Math. 34 (1933) p. 480-508.

G. S. RINHART, Note on global dimension of a certain ring Proc. Am. Math. Soc. 13(1962). p. 341-346.

A ROY, A note on filtered rings, Arch. der. Math. 16 (1965) p. All-All.