Acta Mathematica

  • Acta Math.
  • Volume 104, Number 3-4 (1960), 163-215.

A structure theory for a class of lattice-ordered rings

D. G. Johnson

Full-text: Open access

Note

This paper is based on the author's doctoral dissertation, written under the supervision of Prof. Melvin Henriksen. The author wishes to thank Prof. Henriksen for his advice and encouragement. Financial support for this research was provided by the National Science Foundation, U.S.A., under contract No. NSF G-3021. and by the Office of Naval Research, U. S. Navy, under contract No. Nonr 1100(12).

Article information

Source
Acta Math. Volume 104, Number 3-4 (1960), 163-215.

Dates
Received: 11 June 1959
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485889160

Digital Object Identifier
doi:10.1007/BF02546389

Zentralblatt MATH identifier
0094.25305

Rights
1960 © Almqvist & Wiksells Boktryckeri

Citation

Johnson, D. G. A structure theory for a class of lattice-ordered rings. Acta Math. 104 (1960), no. 3-4, 163--215. doi:10.1007/BF02546389. https://projecteuclid.org/euclid.acta/1485889160


Export citation

References

  • Artin, E., Geometric Algebra. Interscience, New York, 1957.
  • Birkhoff, G., Lattice Theory, Rev. ed., Colloquium Publication no. 25, Amer. Math. Soc., New York, 1948.
  • Birkhoff, G. & Pierce, R. S., Lattice-ordered rings. An. Acad. Brasil. Ci., 28 (1956), 41–69.
  • Bourbaki, N., Algèbre. (Chap. VI.) Actualités Scientifiques et Industrielles, no. 1179, Paris, 1952.
  • Brainerd, B., On a class of lattice-ordered rings. Proc. Amer. Math. Soc., 8 (1957). 673–683.
  • Brown, B. & McCoy, N. H., Rings with unit element which contain a given ring. Duke Math. J., 13 (1946), 9–20.
  • Chehata, C. G., On an ordered semigroup. J. London Math. Soc., 28 (1953), 353–356.
  • Divinsky, N., Commutative subdirectly irreducible rings. Proc. Amer. Math. Soc., 8 (1957), 642–648.
  • Dorroh, J. L., Concerning adjunctions to algebras. Bull. Amer. Math. Soc., 38 (1932), 85–88.
  • Gillman, L. & Henriksen, M., Concerning rings of continuous functions. Trans. Amer. Math. Soc., 77 (1954), 340–362.
  • Hion, Ya. V., Archimedean ordered rings. Uspehi Mat. Nauk (N. S.), 9 (1954), 237–242 (Russian); Math. Rev. vol. 16, p. 442.
  • —, Ordered associative rings. Dokl. Akad. Nauk SSSR (N. S.), 101 (1955), 1005–1007. (Russian); Math. Rev. vol. 17, p. 8.
  • Jacobson, N., Structure of Rings. Colloquium Publication no. 37, Amer. Math. Soc., Providence, 1956.
  • Jaffard, P., Contribution à l'étude des groupes ordonnés. J. Math. Pures Appl., 32 (1953), 203–280.
  • Johnson, R. E., On ordered domains of integrity. Proc. Amer. Math. Soc., 3 (1952), 414–416.
  • Malcev, A., On the immersion of an algebraic ring into a field. Math. Ann., 113 (1936), 686–691.
  • McCoy, N. H., Subdirectly irreducible commutative rings. Duke Math. J., 12 (1945), 381–387.
  • —, Rings and Ideals. Carus Monograph no. 8, Math. Assoc. of Amer., Buffalo, 1948.
  • —, Prime ideals in general rings. Amer. J. Math., 71 (1949), 823–833.
  • Pierce, R. S., Radicals in function rings. Duke Math. J., 23 (1956), 253–261.
  • Szendrel, J., On the extension of rings without divisors of zero. Acta Univ. Szeged., 13 (1950), 231–234.
  • Vinogradov, A. A., On the theory of ordered semigroups. Ivanov. Gos. Ped. Inst. Uč. Zap. Fiz.-Mat. Nauki, 4 (1953), 19–21 (Russian); Math. Rev. vol. 17, p. 710.
  • van der Waerden, B. L., Algebra I. Springer, Berlin, 1955.