Introduction. The purpose of this paper is to extend some of the author's results [4; 51 about F-rings to a wider class of lattice ordered rings called generalized F-rings. A generalized F-ring or GFR is a partially ordered real algebra R which forms a a-complete vector lattice with respect to addition, scalar multiplication, and order, and for which the following statements are valid: (GI) For a, bEER with a>O, bO, ab=ONaAb=O. (G2) For each aER there exists an ideal I of R such that aGI and I possesses a unit element. An arbitrary ring satisfying G2 is called a ring with local unit. Such rings have been previously studied by Morrison [12]. It is possible that many of the results of [4; 5] can be proved for GFR's by a direct attempt to reproduce the arguments of [4; 5 ] in the wider setting. Instead, however, it is shown that every GFR can be embedded in an F-ring and then this result is used to generalize the results of [4; 5]. We prove the embedding theorem for the more general class of rings with local unit. In particular, in ?1, a construction is given for the normalizer of a ring with local unit which involves an inverse limit process. As a corollary we show that the normalizer of a strongly regular ring is also strongly regular. The normalizer N of a faithful ring R is the maximal subring of the ring C of endomorphisms of R (considered as a left R-module) relative to the condition that N contain R as an ideal. This concept has been studied extensively by Johnson. See for example [ll]. The normalizer of a GFR is again a GFR, and since it contains an identity, it is an F-ring. In ?2, a certain class of f-rings is shown to be embeddable in our F-rings. Birkhoff and Pierce [31 define an f-ring to be a lattice-ordered ring in which aAb=O and c>O imply caAb=acAb=0. ?3 deals with the relationship between a GFR and its conditionally u-complete Boolean ring of idempotents. It should be remarked at this point that no distinction is made here between a Boolean ring and a relatively complemented distributive lattice with zero, since a homomorphism which preserves one of these structures also preserves the other. A number of results of