An embedding theorem for commutative lattice-ordered domains
HTML articles powered by AMS MathViewer
- by Stuart A. Steinberg PDF
- Proc. Amer. Math. Soc. 31 (1972), 409-416 Request permission
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.References
- F. W. Anderson, Lattice-ordered rings of quotients, Canadian J. Math. 17 (1965), 434–448. MR 174600, DOI 10.4153/CJM-1965-044-7
- Paul Conrad, The lattice of all convex $l$-subgroups of a lattice-ordered group, Czechoslovak Math. J. 15(90) (1965), 101–123 (English, with Russian summary). MR 173716
- Paul Conrad and John Dauns, An embedding theorem for lattice-ordered fields, Pacific J. Math. 30 (1969), 385–398. MR 246859
- P. F. Conrad and J. E. Diem, The ring of polar preserving endomorphisms of an abelian lattice-ordered group, Illinois J. Math. 15 (1971), 222–240. MR 285462
- Paul Conrad, John Harvey, and Charles Holland, The Hahn embedding theorem for abelian lattice-ordered groups, Trans. Amer. Math. Soc. 108 (1963), 143–169. MR 151534, DOI 10.1090/S0002-9947-1963-0151534-0
- J. E. Diem, A radical for lattice-ordered rings, Pacific J. Math. 25 (1968), 71–82. MR 227068
- László Fuchs, Teilweise geordnete algebraische Strukturen, Studia Mathematica/Mathematische Lehrbücher, Band XIX, Vandenhoeck & Ruprecht, Göttingen, 1966 (German). Übersetzt aus dem Englischen von Éva Vas. MR 0204547
- Stuart A. Steinberg, Finitely-valued $f$-modules, Pacific J. Math. 40 (1972), 723–737. MR 306078 E. C. Weinberg, Lectures on ordered groups and rings, Lecture Notes, University of Illinois, Urbana, Illinois, 1968.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 409-416
- DOI: https://doi.org/10.1090/S0002-9939-1972-0285464-1
- MathSciNet review: 0285464