The Congruences of a Finite Lattice A "Proof-by-Picture" Approach /

• Κύριος συγγραφέας: Grätzer, George (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Έκδοση: 2nd ed. 2016.
• Θέματα: Mathematics.; Algebra.; Ordered algebraic structures.; Mathematical logic.; Number theory.; Probabilities.; Order, Lattices, Ordered Algebraic Structures.; Mathematical Logic and Foundations.; Probability Theory and Stochastic Processes.; Number Theory.

This 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 te...

Πίνακας περιεχομένων:

• 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.