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Additional Topics

  • Stuart A. Steinberg
Chapter

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.

Keywords

Partial Order Total Order Matrix Algebra Division Ring Additional Topic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ToledoToledoUSA

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