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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An embedding theorem for commutative lattice-ordered domains

Author: Stuart A. Steinberg
Journal: Proc. Amer. Math. Soc. 31 (1972), 409-416
MathSciNet review: 0285464
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Abstract: In a recent paper Conrad and Dauns have shown that a finitely-rooted lattice-ordered field $ R$, in which multiplication by a positive special element is a lattice homomorphism, can be embedded in a formal power series $ l$-field with real coefficients, provided that the value group of $ R$ is torsion-free. In this note it is shown that their theorem is true when $ R$ is a commutative integral domain.

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Keywords: Lattice-ordered ring, commutative domain, formal power series, classical ring of quotients, value preserving $ l$-isomorphism, finitely-valued $ l$-group, special element
Article copyright: © Copyright 1972 American Mathematical Society