Lattice-ordered Rings and Modules

This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and accessible to a variety of readers is included. Key topics include: lattice-ordered groups, rings, and fields; Archimedean l-groups; f-rings and larger varieties of l-rings; the category of f-modules; various commutativity results. This text may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules.