The Additive Group of an f-ring

Abstract

The intent of this paper is to show that the additive l-group of an f-ring S determines the ring structure. This is why there are so many papers that simply extend known results for abelian l-groups to f-rings. Theorem 3.1 asserts that there is a one-to-one correspondence between the f-multiplications on S and a set of homomorphisms from the positive cone of the l-group S into the positive cone of the ring (S) of polar preserving endomorphisms of the l-group S. In fact, each f-multiplication of S is determined by a homomorphism of S+ into (S)+.