Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T16:13:08.989Z Has data issue: false hasContentIssue false
  • English
  • Français

A finiteness theorem in homological algebra

Published online by Cambridge University Press:  24 October 2008

J. F. Adams
J. F. Adams
Affiliation:
Trinity HallCambridge
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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