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Lattice-ordered Rings and Modules [electronic resource] /by Stuart A. Steinberg.

by Steinberg, Stuart A [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: New York, NY : Springer New York, 2010.Edition: First.Description: online resource.ISBN: 9781441917218.Subject(s): Mathematics | Algebra | Mathematics | Order, Lattices, Ordered Algebraic Structures | Algebra | Non-associative Rings and AlgebrasDDC classification: 511.33 Online resources: Click here to access online
Contents:
Partially Ordered Sets and Lattices -- Lattice-ordered Groups -- Lattice-ordered Rings -- The Category of -Modules -- Lattice-ordered Fields -- Additional Topics.
In: Springer eBooksSummary: 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.
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Partially Ordered Sets and Lattices -- Lattice-ordered Groups -- Lattice-ordered Rings -- The Category of -Modules -- Lattice-ordered Fields -- Additional Topics.

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.

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