## The Congruences of a Finite Lattice: A "Proof-by-Picture" ApproachThis is a self-contained 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 Proof-by-Picture method. Key features: * Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving 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 yearsThe book is appropriate for a one-semester graduate course in lattice theory, and it is a practical reference for researchers studying lattices.
(Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007)
"The book is self-contained, with many detailed proofs presented that can be followed step-by-step. [I]n addition to giving the full formal details of the proofs, the author chooses a somehow more pedagogical way that he calls Proof-by-Picture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. I believe that this book is a much-needed 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 |

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### Contents

2 | |

Part
II Some Special Techniques | 54 |

Part
III Congruence Lattices of Finite Lattices | 86 |

Part
IV Congruence Lattices and Lattice Extensions | 154 |

Part
V Congruence Lattices of Two Related Lattices | 223 |

Part
VI The Ordered Set of Principal Congruences | 273 |

Part
VII Congruence Structure | 288 |

322 | |

337 | |

### Other editions - View all

The Congruences of a Finite Lattice: A "Proof-by-Picture" Approach George Grätzer No preview available - 2016 |