Archimedean, semiperfect and 𝜋-regular lattice-ordered algebras with polynomial constraints are 𝑓-algebras

Steinberg, Stuart A.

doi:10.1090/S0002-9939-1983-0712623-0

Archimedean, semiperfect and $\pi$-regular lattice-ordered algebras with polynomial constraints are $f$-algebras
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by Stuart A. Steinberg

Proc. Amer. Math. Soc. 89 (1983), 205-210

DOI: https://doi.org/10.1090/S0002-9939-1983-0712623-0

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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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