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Observations on the Künneth theorem

Published online by Cambridge University Press:  24 October 2008

G. M. Kelly
G. M. Kelly
Affiliation:
University of Sydney, Australia
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Extract

Let A be a right Λ-complex and C be a left Λ-complex where Λ is a ring which is both left and right hereditary; a principal ideal domain is a special case of such a ring. This paper is concerned with the Künneth theorem expressing the homology H(A⊗C) of the product complex A⊗C (= A⊗ΛC) in terms of H(A) and H(C). Any notations we do not explain are those of (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 575 - 587
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Cartan, H. and Eilenberg, S., Homological algebra (Princeton, 1956).Google Scholar
(2)Eilenberg, S. and MacLane, S., On the groups H(π, n). II. Ann. of Math. 60 (1954), 49–139.CrossRefGoogle Scholar
(3)MacLane, S., Triple torsion products and multiple Künneth formulas. Math. Ann. 140 (1960), 51–64.CrossRefGoogle Scholar