Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Category and group rings in homotopy theory
HTML articles powered by AMS MathViewer

by William J. Ralph PDF
Trans. Amer. Math. Soc. 299 (1987), 205-223 Request permission


It frequently arises in algebraic topology that a function $\beta :G \to H$, between two groups, is not a homomorphism. We show that in many standard situations $\beta$ induces a group homomorphism $\overline \beta :{\mathbf {Z}}(G)/{\mathcal {A}^d} \to H$, where ${\mathcal {A}^d}$ is a power of the augumentation ideal in the group ring ${\mathbf {Z}}(G)$. A typical example is $\beta :[X, Y] \to [{S^2}X, {S^2}Y]$ where $Y$ is some $H$-group, in which case $d$ can be taken to be $1 + {\text {cat}} X$.
  • Max Karoubi, $K$-theory, Grundlehren der Mathematischen Wissenschaften, Band 226, Springer-Verlag, Berlin-New York, 1978. An introduction. MR 0488029
  • William J. Ralph, An extension of singular homology to Banach algebras, Pacific J. Math. 123 (1986), no. 2, 391–405. MR 840850
  • James Stasheff, $H$-spaces from a homotopy point of view, Lecture Notes in Mathematics, Vol. 161, Springer-Verlag, Berlin-New York, 1970. MR 0270372
  • Robert M. Switzer, Algebraic topology—homotopy and homology, Die Grundlehren der mathematischen Wissenschaften, Band 212, Springer-Verlag, New York-Heidelberg, 1975. MR 0385836
  • George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 55Q05, 55P50
  • Retrieve articles in all journals with MSC: 55Q05, 55P50
Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 299 (1987), 205-223
  • MSC: Primary 55Q05; Secondary 55P50
  • DOI:
  • MathSciNet review: 869408