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On lattice-ordered rings in which the square of every element is positive

Published online by Cambridge University Press:  09 April 2009

Stuart A. Steinberg
Stuart A. Steinberg
Affiliation:
University of Toledo, Toledo, Ohio, 43606, U.S.A.
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Abstract

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It is shown that a unital lattice-ordered ring in which the square of every element is positive is embeddable in a product of totally ordered rings provided it is archimedean, semiperfect, or π-regular. Also, some canonical examples of unital l-domains with squares positive that are not totally ordered are discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 3 , November 1976 , pp. 362 - 370
Copyright
Copyright © Australian Mathematical Society 1976

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