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A theorem of homological algebra

Published online by Cambridge University Press:  24 October 2008

D. Rees
D. Rees
Affiliation:
Downing CollegeCambridge
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Extract

The present note is concerned with the proof and applications of the following theorem: Let A be a commutative ring, N be an A-module, and g1, …, gk be elements of A such that (g1,…, gi−1) A:gi = (g1,…, gi−1) N:gi = (g1,…, gi−1) N (i = 1,…, k), so that 0:g1 = 0 in N. Let g denote the ideal (g1 …, gk), let B = A/g and let M be any A-module such that gM = 0. then

where, on the right-hand side of (ii), M, N/gN are considered as B-modules.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 4 , October 1956 , pp. 605 - 610
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Cartan, H. and Eilenberg, S.Homological algebra (Princeton). (To be published shortly.)Google Scholar
(2)Serre, J.-P.Faisceaux algebriques coherent. Ann. Math., Princeton, 61 (1955), 197–278.CrossRefGoogle Scholar