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Mathematics - Algebra | Lattices and Ordered Sets

Lattices and Ordered Sets

Roman, Steven

2009, XV, 305 p.

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  • Written in an appealing style
  • Will become a standard text and an invaluable guide
  • Contains a plethora of exercises, examples, and illustrations

This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area.

 

The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises.

 

Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more.

 

Steven Roman is the author of many successful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), Field Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004).

Content Level » Graduate

Keywords » Abstract algebra - Lattice - algebra - category theory

Related subjects » Algebra

Table of contents 

Basic Theory.- Partially Ordered Sets.- Well-Ordered Sets.- Lattices.- Modular and Distributive Lattices.- Boolean Algebras.- The Representation of Distributive Lattices.- Algebraic Lattices.- Prime and Maximal Ideals; Separation Theorems.- Congruence Relations on Lattices.- Topics.- Duality for Distributive Lattices: The Priestley Topology.- Free Lattices.- Fixed-Point Theorems.

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