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Simple reduction theorems for extension and torsion functors

Published online by Cambridge University Press:  24 October 2008

D. G. Northcott
D. G. Northcott
Affiliation:
The UniversitySheffield
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Extract

Let Λ be a commutative ring with an identity element and c an element of Λ which is not a zero divisor Denote by Ω the residue class ring Λ/Λc. If now M is a Λ-module for which c is not a zero divisor, and A is an Ω-module, then a theorem of Rees (2) asserts that, for every non-negative integer n, we have a Λ-isomorphism

This reduction theorem has found a number of useful and interesting applications.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 483 - 488
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Cartan, H. and Eilenberg, S.Homological algebra (Princeton 1956).Google Scholar
(2)Rees, D.A theorem of homological algebra. Proc. Camb. Phil. Soc. 52 (1956), 605–10.CrossRefGoogle Scholar