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. 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.
Steinberg presents the material through 800+ extensive examples
of varying levels of difficulty along with numerous exercises at
the end of each section. 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.
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