J Austral Math Soc Ser A 48 pp359--375, 1990.

Vector Lattices Over Subfields of the Reals

P. Bixler, P. Conrad, W. B. Powell and C. Tsinakis

Abstract

In this paper we consider classes of vector lattices over subfields of the real numbers. Among other properties we relate the archimedean condition of such a vector lattice to the uniqueness of scalar multiplication and the linearity of l-automorphisms. If a vector lattice in the classes considered admits an essential subgroup that is not a minimal prime, then it also admits a non-linear l-automorphism and more than one scalar multiplication. It is also shown that each l-group contains a largest archimedean convex l-subgroup which admits a unique scalar multiplication.

1980 AMS Subject Classification (1985 Revision): 06F20

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Authors

P. Bixler

Department of Computer Science, Virginia Polytechnic Institute, Blacksburg, Virginia 24061, U.S.A.

P. Conrad

University of Kansas, Lawrence, Kansas 66044, U.S.A.

W. B. Powell

Oklahoma State University, Stillwater, Oklahoma 74078, U.S.A.

C. Tsinakis

Vanderbilt University, Nashville, Tennessee 37235, U.S.A.