A Survey of f-Rings and Some of their Generalizations

What follows is an incomplete survey of the topic of the title that reflects the biases of the author. It focuses mainly on structure theory and neglects questions of mathematical logic, as well as generalizations to non associative rings, near rings, or more general algebraic systems. Neglected also are papers written in Chinese or Russian that do not include proofs and appear in journals difficult or impossible to obtain locally. While totally ordered rings and the ring C(X) of continuous real-valued functions on a topological space X are important examples of f-rings, these areas will be mentioned only in passing. For a recent survey of the former, see [He1]. Homological and categorical considerations will be taken up only briefly because of the ignorance of the author, and I am unaware of significant activity about sheaves and f-rings other than what is listed in [BKW]. Readers who have access to Mathematical Reviews on disc or on the Internet should be able to locate summaries of missing papers by searching under “f-rings”, “lattice ordered rings”, or variations on these themes