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Additional Topics

In: Lattice-ordered Rings and Modules

Author

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  • Stuart A. Steinberg

    (University of Toledo, Department of Mathematics)

Abstract

Two themes that occur in this chapter concern the attempt to describe all lattice orders of a particular type on some familiar rings and the attempt to recognize some familiar lattice-ordered rings. Thus, a characterization is given of the real group ℓ-algebra of a locally finite group with the coordinatewise partial order and of the canonically ordered ℓ-group ring of a finite cyclic group with coefficients in a matrix ring over a totally ordered field. All of the lattice orders of a matrix algebra over a totally ordered subfield of the reals and of a 2×2 matrix algebra over any totally ordered field are determined. Also, for a polynomial ring in one variable over an ℓ-simple totally ordered Öre domain all nontotal lattice orders which extend the order of the coefficient ring and in which all squares are positive are described. This description is a specialization of a description of some lattice orders on a semigroup ring over a mopops.

Suggested Citation

  • Stuart A. Steinberg, 2010. "Additional Topics," Springer Books, in: Lattice-ordered Rings and Modules, edition 0, chapter 0, pages 511-607, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-1721-8_6
    DOI: 10.1007/978-1-4419-1721-8_6
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