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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Beware the phony multiplication on Quillen’s $\mathcal {A}^{-1}\mathcal {A}$
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by R. W. Thomason PDF
Proc. Amer. Math. Soc. 80 (1980), 569-573 Request permission

Abstract:

This paper exposes a subtle but irreparable flaw in a frequently proposed construction of the graded ring structure on the algebraic K-groups of commutative rings.
References
  • Samuel Eilenberg and G. Max Kelly, Closed categories, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 421–562. MR 0225841
  • Zbigniew Fiedorowicz, The Quillen-Grothendieck construction and extension of pairings, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977) Lecture Notes in Math., vol. 657, Springer, Berlin, 1978, pp. 163–169. MR 513547, DOI 10.1007/BFb0069233
  • Daniel Grayson, Higher algebraic $K$-theory. II (after Daniel Quillen), Algebraic $K$-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976) Lecture Notes in Math., Vol. 551, Springer, Berlin, 1976, pp. 217–240. MR 0574096
  • J. L. Loday, K-théorie algébrique et représentations de groups, Ann. Sci. École Norm. Sup. (4) 9 (1976).
  • Saunders MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York-Berlin, 1971. MR 0354798
  • J. Peter May, $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra, Lecture Notes in Mathematics, Vol. 577, Springer-Verlag, Berlin-New York, 1977. With contributions by Frank Quinn, Nigel Ray, and Jørgen Tornehave. MR 0494077
  • J. P. May, $E_{\infty }$ spaces, group completions, and permutative categories, New developments in topology (Proc. Sympos. Algebraic Topology, Oxford, 1972) London Math. Soc. Lecture Note Ser., No. 11, Cambridge Univ. Press, London, 1974, pp. 61–93. MR 0339152
  • J. P. May, $H_{\infty }$ ring spectra and their applications, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 229–243. MR 520544
  • Graeme Segal, Categories and cohomology theories, Topology 13 (1974), 293–312. MR 353298, DOI 10.1016/0040-9383(74)90022-6
  • Robert W. Thomason, First quadrant spectral sequences in algebraic $K$-theory via homotopy colimits, Comm. Algebra 10 (1982), no. 15, 1589–1668. MR 668580, DOI 10.1080/00927878208822794
  • Friedhelm Waldhausen, Algebraic $K$-theory of generalized free products. I, II, Ann. of Math. (2) 108 (1978), no. 1, 135–204. MR 498807, DOI 10.2307/1971165
  • R. Wolfson, Higher $\Gamma$-spaces and hyperspectra, Quart J. Math. Oxford Ser. 30 (1979), 229-255.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 80 (1980), 569-573
  • MSC: Primary 18F25; Secondary 55N45, 55S99
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0587929-6
  • MathSciNet review: 587929