Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Ido Efrat
Title: Valuations, orderings and Milnor $ K$-theory
Additional book information: Mathematical Surveys and Monographs, vol. 124, American Mathematical Society, Providence, RI, 2006, xiv+288 pp., ISBN 978-0-8218-4041-2, US$60.00$

References [Enhancements On Off] (What's this?)

  • Jón Kr. Arason, Richard Elman, and Bill Jacob, Rigid elements, valuations, and realization of Witt rings, J. Algebra 110 (1987), no. 2, 449–467. MR 910395, DOI 10.1016/0021-8693(87)90057-3
  • Eberhard Becker and Ludwig Bröcker, On the description of the reduced Witt ring, J. Algebra 52 (1978), no. 2, 328–346. MR 506029, DOI 10.1016/0021-8693(78)90243-0
  • Eberhard Becker and Alex Rosenberg, Reduced forms and reduced Witt rings of higher level, J. Algebra 92 (1985), no. 2, 477–503. MR 778463, DOI 10.1016/0021-8693(85)90135-8
  • Ludwig Bröcker, Zur Theorie der quadratischen Formen über formal reellen Körpern, Math. Ann. 210 (1974), 233–256 (German). MR 354549, DOI 10.1007/BF01350587
  • Ludwig Bröcker, Characterization of fans and hereditarily Pythagorean fields, Math. Z. 151 (1976), no. 2, 149–163. MR 422233, DOI 10.1007/BF01213992
  • Thomas C. Craven, Characterizing reduced Witt rings of fields, J. Algebra 53 (1978), no. 1, 68–77. MR 480332, DOI 10.1016/0021-8693(78)90205-3
    • [E]
    I. Efrat, Orderings, valuations and free products of Galois groups, Sém. Struct. Alg. Ordonnées 54, Univ. Paris 7 (1995).
  • Yoon Sung Hwang and Bill Jacob, Brauer group analogues of results relating the Witt ring to valuations and Galois theory, Canad. J. Math. 47 (1995), no. 3, 527–543. MR 1346152, DOI 10.4153/CJM-1995-029-4
  • Bill Jacob and Roger Ware, A recursive description of the maximal pro-$2$ Galois group via Witt rings, Math. Z. 200 (1989), no. 3, 379–396. MR 978598, DOI 10.1007/BF01215654
  • Bill Jacob and Roger Ware, Realizing dyadic factors of elementary type Witt rings and pro-$2$ Galois groups, Math. Z. 208 (1991), no. 2, 193–208. MR 1128705, DOI 10.1007/BF02571520
  • Jochen Koenigsmann, From $p$-rigid elements to valuations (with a Galois-characterization of $p$-adic fields), J. Reine Angew. Math. 465 (1995), 165–182. With an appendix by Florian Pop. MR 1344135, DOI 10.1515/crll.1995.465.165
  • Mieczysław Kula, Fields with prescribed quadratic form schemes, Math. Z. 167 (1979), no. 3, 201–212. MR 539104, DOI 10.1007/BF01174801
  • Tsit Yuen Lam, Orderings, valuations and quadratic forms, CBMS Regional Conference Series in Mathematics, vol. 52, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1983. MR 714331, DOI 10.1090/cbms/052
  • M. Marshall, The elementary type conjecture in quadratic form theory, Algebraic and arithmetic theory of quadratic forms, Contemp. Math., vol. 344, Amer. Math. Soc., Providence, RI, 2004, pp. 275–293. MR 2060204, DOI 10.1090/conm/344/06224
  • M. Marshall, Real reduced multirings and multifields, J. Pure Appl. Algebra 205 (2006), no. 2, 452–468. MR 2203627, DOI 10.1016/j.jpaa.2005.07.011
  • A. S. Merkur′ev and A. A. Suslin, $K$-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 5, 1011–1046, 1135–1136 (Russian). MR 675529
  • John Milnor, Algebraic $K$-theory and quadratic forms, Invent. Math. 9 (1969/70), 318–344. MR 260844, DOI 10.1007/BF01425486
  • Ján Mináč and Tara L. Smith, Decomposition of Witt rings and Galois groups, Canad. J. Math. 47 (1995), no. 6, 1274–1289. MR 1370518, DOI 10.4153/CJM-1995-065-0
  • Albrecht Pfister, Quadratische Formen in beliebigen Körpern, Invent. Math. 1 (1966), 116–132 (German). MR 200270, DOI 10.1007/BF01389724
  • Victoria Powers, Characterizing reduced Witt rings of higher level, Pacific J. Math. 128 (1987), no. 2, 333–347. MR 888522
  • Alexander Prestel, Lectures on formally real fields, Lecture Notes in Mathematics, vol. 1093, Springer-Verlag, Berlin, 1984. MR 769847, DOI 10.1007/BFb0101548
  • Vladimir Voevodsky, Reduced power operations in motivic cohomology, Publ. Math. Inst. Hautes Études Sci. 98 (2003), 1–57. MR 2031198, DOI 10.1007/s10240-003-0009-z
    • [V2]
    -, On motivic cohomology with $ \mathbb{Z}/\ell $-coefficients, preprint.
    [W]
    E. Witt, Theorie der Quadratischen Formen in beliebigen Körpern, J. Reine Angew. Math. 176 (1937), 31-44.
    Review Information:

    Reviewer: Murray Marshall
    Affiliation: University of Saskatchewan
    Email: marshall@math.usask.ca
    Journal: Bull. Amer. Math. Soc. 45 (2008), 439-444
    Published electronically: August 3, 2007
    Review copyright: © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.