Lattice-ordered Rings and Modules - Steinberg, Stuart A.; SpringerLink (Online service) (New York, NY : Springer New York : Imprint: Springer, 2010)
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. Steinberg includes in his presentation of the material 800+ extensive exercises of varying levels of difficulty at the end of each of the sections. The first two chapters of the book provide a thorough introduction to the material, while the following four chapters delve into more specific topics. 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. Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules.
Partially Ordered Sets and Lattices -- Lattice-ordered Groups -- Lattice-ordered Rings -- The Category of -Modules -- Lattice-ordered Fields -- Additional Topics.
Keywords: Algebra; Ordered algebraic structures; Associative rings; Rings (Algebra).; Algebra; Order, Lattices, Ordered Algebraic Structures; Associative Rings and Algebras