The Congruences of a Finite Lattice: A "Proof-by-Picture" Approach
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Beschreibung
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.
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