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.


Composition algebras over rings of genus zero
HTML articles powered by AMS MathViewer

by S. Pumplün PDF
Trans. Amer. Math. Soc. 351 (1999), 1277-1292 Request permission


The theory of composition algebras over locally ringed spaces and some basic results from algebraic geometry are used to characterize composition algebras over open dense subschemes of curves of genus zero.
  • Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
  • Stanisław Balcerzyk and Tadeusz Józefiak, Commutative Noetherian and Krull rings, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester; distributed by Prentice Hall, Inc., Englewood Cliffs, NJ, 1989. Translated from the Polish by Maciej Juniewicz and Sergiusz Kowalski. MR 1130610
  • F. van der Blij and T. A. Springer, The arithmetics of octaves and of the group $G_{2}$, Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math. 21 (1959), 406–418. MR 0152555
  • J. van Geel, Applications of the Riemann-Roch theorem for curves to quadratic forms and division algebras, UCL, Recherches de math. 7 (1991), 1–32.
  • Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
  • N. Jacobson, Composition algebras and their automorphisms, Rend. Circ. Mat. Palermo (2) 7 (1958), 55–80. MR 101253, DOI 10.1007/BF02854388
  • Manfred Knebusch, Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen, S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1969/70 (1969/1970), 93–157 (German). MR 0271118
  • M.-A. Knus, R. Parimala, and R. Sridharan, On compositions and triality, J. Reine Angew. Math. 457 (1994), 45–70. MR 1305278, DOI 10.1515/crll.1994.457.45
  • B. Küting, Kompositionsalgebren über rationalen Funktionenkörpern, Dissertation. Fern Universität, Hagen, 1987.
  • T. Y. Lam, Serre’s conjecture, Lecture Notes in Mathematics, Vol. 635, Springer-Verlag, Berlin-New York, 1978. MR 0485842
  • Kevin McCrimmon, Nonassociative algebras with scalar involution, Pacific J. Math. 116 (1985), no. 1, 85–109. MR 769825
  • James S. Milne, Étale cohomology, Princeton Mathematical Series, No. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
  • Holger P. Petersson, Composition algebras over algebraic curves of genus zero, Trans. Amer. Math. Soc. 337 (1993), no. 1, 473–493. MR 1108613, DOI 10.1090/S0002-9947-1993-1108613-X
  • Holger P. Petersson, Composition algebras over a field with a discrete valuation, J. Algebra 29 (1974), 414–426. MR 364380, DOI 10.1016/0021-8693(74)90078-7
  • Albrecht Pfister, Quadratic lattices in function fields of genus $0$, Proc. London Math. Soc. (3) 66 (1993), no. 2, 257–278. MR 1199066, DOI 10.1112/plms/s3-66.2.257
  • S. Pumplün, Composition algebras over open dense subschemes of curves of genus zero, Non-Associative Algebra and its Applications (Santos Gonzalez, ed.). Kluwer Academic Publishers, Dordrecht, 1994, pp. 341–343.
  • S. Pumplün, Kompositionsalgebren über Ringen vom Geschlecht Null. Dissertation, Fern Universität, Hagen, 1995.
  • I. Reiner, Maximal orders, London Mathematical Society Monographs, No. 5, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1975. MR 0393100
  • Winfried Scharlau, Quadratic and Hermitian forms, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 270, Springer-Verlag, Berlin, 1985. MR 770063, DOI 10.1007/978-3-642-69971-9
  • A. Tillmann, Unzerlegbare Vektorbündel über algbraischen Kurven, Dissertation. Fern Universität, Hagen, 1983.
  • E. Witt, Über ein Gegenbeispiel zum Normensatz, Math. Z. 39 (1934), 462–467.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 17A75, 14H99
  • Retrieve articles in all journals with MSC (1991): 17A75, 14H99
Additional Information
  • S. Pumplün
  • Affiliation: Fakultät für Mathematik, Universität Regensburg, Universitätsstr. 31, 93040 Regensburg, Germany
  • Address at time of publication: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
  • MR Author ID: 364237
  • Email:
  • Received by editor(s): February 20, 1996
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1277-1292
  • MSC (1991): Primary 17A75; Secondary 14H99
  • DOI:
  • MathSciNet review: 1422907