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Homology of Non-Commutative Polynomial Rings

Published online by Cambridge University Press:  22 January 2016

R. Sridharan
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Let Γ be a ring with unit element and let Λ be the Ore extension of Γ with respect to a derivation d of Γ [4, 3]. It is shown in [3] that l.gl. dim Λ ≦ 1 + l.gl. dim Γ. It is not in general possible to replace this inequality by equality.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 26 , February 1966 , pp. 53 - 59
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton University Press, 1956.Google Scholar
[2] Eilenberg, S., Rosenberg, A. and Zelinsky, D.: On the dimension of modules and algebras VIII, Nagoya Math. J. 12, 71–93 (1957).CrossRefGoogle Scholar
[3] Gopalakrishnan, N. S.: On some filtered rings. Proc. Ind. Acad. Sci. 56, 148–54 (1962).Google Scholar
[4] Ore, O.: Theory of non-commutative polynomials. Annals of Mathematics. 34, 480–508 (1933).CrossRefGoogle Scholar
[5] Rinehart, G. S.: Note on the global dimension of certain rings Proc. Amer .Math. Soc., 13, 341–46 (1962).Google Scholar
[6] Roy, A.: A note on filtered rings (to appear).CrossRefGoogle Scholar