Archimedean, semiperfect and 𝜋-regular lattice-ordered algebras with polynomial constraints are 𝑓-algebras
Stuart A. Steinberg · Proceedings of the American Mathematical Society · 1983
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 f -element, and satisfies a polynomial identity p ( x ) ⩾ 0 p(x) \geqslant 0 or f ( x , y ) ⩾ 0 f(x,y) \geqslant 0 (for suitable f ( x , y ) f(x,y) ); or (ii) it is unital, and semiperfect, π \pi -regular, or left π \pi -regular, and some power of each element is positive.