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Proceedings of the American Mathematical Society

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Archimedean, semiperfect and $ \pi $-regular lattice-ordered algebras with polynomial constraints are $ f$-algebras


Author: Stuart A. Steinberg
Journal: Proc. Amer. Math. Soc. 89 (1983), 205-210
MSC: Primary 06F25; Secondary 16A86
DOI: https://doi.org/10.1090/S0002-9939-1983-0712623-0
MathSciNet review: 712623
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Abstract: It is shown that a lattice-ordered algebra is embeddable in a product of totally ordered algebras provided (i) it is archimedean, contains a left superunit which is an $ f$-element, and satisfies a polynomial identity $ p(x) \geqslant 0$ or $ f(x,y) \geqslant 0$ (for suitable $ f(x,y)$); or (ii) it is unital, and semiperfect, $ \pi $-regular, or left $ \pi $-regular, and some power of each element is positive.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0712623-0
Keywords: Lattice-ordered ring, totally ordered ring, polynomial constraint
Article copyright: © Copyright 1983 American Mathematical Society