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
- Ichirô Amemiya, A general spectral theory in semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. Ser. I. 12 (1953), 111–156. MR 0056853
- 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).
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