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A finiteness theorem in homological algebra

Published online by Cambridge University Press:  24 October 2008

J. F. Adams
J. F. Adams
Affiliation:
Trinity HallCambridge
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Extract

In (1), (2), (3) and (4) it is shown that homological algebra (5) can be applied to stable homotopy-theory. In this application, we deal with A-modules, where A is the mod p Steenrod algebra. In the present paper, we shall prove a finiteness theorem for the cohomology of the Steenrod algebra. This theorem is stated as Corollary 2 below. It is purely algebraic, but it is not claimed that it has any algebraic interest; it is inspired solely by the application mentioned above. Here it has the following uses.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 1 , January 1961 , pp. 31 - 36
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Adams, J. F., On the structure and applications of the Steenrod algebra. Comment. math. helvet. 32 (1958), 180–214.CrossRefGoogle Scholar
(2)Adams, J. F., On the non-existence of elements of Hopf invariant one. Bull. Amer. Math. Soc. 64 (1958), 279–82.Google Scholar
(3)Adams, J. F., On the non-existence of elements of Hopf invariant one. Ann. Math. 72 (1960), 20–104.Google Scholar
(4)CartanSeminarNotes, 1958–1959.Google Scholar
(5)Cartan, H., and Eilenberg, S., Homological algebra (Princeton, 1956).Google Scholar