Edition 
2nd ed. 
Physical description 
1 online resource (xxxiv, 346 p.) : ill. 
Series 
Springer English/International eBooks 2016  Full Set


Springer Mathematics and Statistics eBooks 2016 English+International

Contents 
I: A Brief Introduction to Lattices  Basic Concepts  Special Concepts  Congruences  Planar Semimodular Lattices  II: Some Special Techniques  Chopped Lattices  Boolean Triples  Cubic Extensions  III: Congruence Lattices of Finite Lattices  The Dilworth Theorem  Minimal Representations  Semimodular Lattices  Rectangular Lattices  Modular Lattices  Uniform Lattices  IV: Congruence Lattices and Lattice Extensions  Sectionally Complemented Lattices  Semimodular Lattices  Isoform Lattices  The Congruence Lattice and the Automorphism Group  Magic Wands  V: Congruence Lattices of Two Related Lattices  Sublattices  Ideals  Tensor Extensions  VI The Ordered Set of Principal Congruences  Representation Theorems  Isotone Maps  VII: Congruence Structure  Prime Intervals and Congruences  Some Applications of the Swing Lemma. 
Summary 
This is a selfcontained exposition by one of the leading experts in lattice theory, George Grätzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature ProofbyPicture method. Key features: * Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruencepreserving extensions * Contains complete proofs, an extensive bibliography and index, and over 140 illustrations * This new edition includes two new parts on Planar Semimodular Lattices and The Order of Principle Congruences, covering the research of the last 10 years The book is appropriate for a onesemester graduate course in lattice theory, and it is a practical reference for researchers studying lattices. Reviews of the first edition: "There exist a lot of interesting results in this area of lattice theory, and some of them are presented in this book. [This] monograph...is an exceptional work in lattice theory, like all the contributions by this author. ... The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. Moreover, the author provides a series of companion lectures which help the reader to approach the ProofbyPicture sections." (Cosmin Pelea, Studia Universitatis BabesBolyai Mathematica, Vol. LII (1), 2007) "The book is selfcontained, with many detailed proofs presented that can be followed stepbystep. [I]n addition to giving the full formal details of the proofs, the author chooses a somehow more pedagogical way that he calls ProofbyPicture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. I believe that this book is a muchneeded tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." Mathematical Reviews. 
Other author 
SpringerLink issuing body.

Subject 
Congruence lattices.


Lattice theory.


Mathematics.


Algebra.


Ordered algebraic structures.


Logic, Symbolic and mathematical.


Number theory.


Probabilities.


Electronic books. 
ISBN 
9783319387987 (electronic bk.) 

3319387987 (electronic bk.) 

9783319387963 (print) 

3319387960 (print) 

9783319387963 (print) 
Standard Number 
10.1007/9783319387987 
