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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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Representation of the projectable and strongly projectable hulls of a lattice-ordered group
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by Donald A. Chambless PDF
Proc. Amer. Math. Soc. 34 (1972), 346-350 Request permission

Abstract:

A representable l-group G can be embedded into a projectable (strongly projectable) l-group; an essential extension of G which is minimal with respect to being projectable (strongly projectable) is unique. In this paper these projectable and strongly projectable “hulls” of G are represented using direct limits. If G is an f-ring, or f-ring without nonzero nilpotent elements, then so are these hulls.
References
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  • S. J. Bernau, Orthocompletion of lattice groups, Proc. London Math. Soc. (3) 16 (1966), 107–130. MR 188113, DOI 10.1112/plms/s3-16.1.107
  • Paul Conrad, The lateral completion of a lattice-ordered group, Proc. London Math. Soc. (3) 19 (1969), 444–480. MR 244125, DOI 10.1112/plms/s3-19.3.444
  • —, Lattice-ordered groups, Tulane University, New Orleans, La., 1970.
  • Paul Conrad, The hulls of representable $l$-groups and $f$-rings, J. Austral. Math. Soc. 16 (1973), 385–415. Collection of articles dedicated to the memory of Hanna Neumann, IV. MR 0344173
  • L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864
  • T. Speed, On lattice-ordered groups, J. Austral. Math. Soc. (to appear).
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 346-350
  • MSC: Primary 06A55
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0295990-7
  • MathSciNet review: 0295990