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Partially Ordered Sets and Lattices. Pages Lattice-ordered Groups. Lattice-ordered Rings. The Category of f -Modules.

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Lattice-ordered Fields. This book would fill in the gap admirably. Any algebraist or functional analyst whose work involves ordered structures would be interested in this book. That includes mathematicians who study: lattices, ordered semigroups, ordered groups, ordered rings, ordered fields, Riesz spaces, vector lattices, or Banach lattices.

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It would also be useful for mathematicians who are interested in general ring theory, general group theory, matrix algebras, or function algebras especially Banach algebras. In short, there is a wide audience who would find the tools that this book provides very useful. Lattice-ordered rings and modules is the latest in a line of books aimed at simultaneously detailing the history while up-dating the canon of the theory of lattice-ordered groups and rings. The author has been able to create a book that is both accessible to graduate students and useful to researchers.

Warren Wm. McGovern, Mathematical Reviews, Issue b This book gives a comprehensive account of the algebraic aspects of the theories of lattice-ordered rings and those lattice-ordered modules which can be embedded in a product of totally ordered modules, the f-modules. It is written at a level suitable for gifted second-year graduate students in mathematics and A list of 27 open problems concludes the book, which will be the text of reference to lattice-ordered rings and modules for many years to come.

Mitsch, Monatshefte fur Mathematik, Vol. Another advantage of the book is that at the end of every chapter there is a useful Note which provides the references used in the chapter. Finally, the book ends with 27 interesting open problems.

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Lecture Notes on Algebraic Structure of Lattice Ordered Rings

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