LEADER 04686nam 2200577 450 001 9910683352303321 005 20231115180108.0 010 $a9783031290633$b(electronic bk.) 010 $z9783031290626 024 7 $a10.1007/978-3-031-29063-3 035 $a(MiAaPQ)EBC7219456 035 $a(Au-PeEL)EBL7219456 035 $a(OCoLC)1374429249 035 $a(DE-He213)978-3-031-29063-3 035 $a(PPN)26910089X 035 $a(EXLCZ)9926313111300041 100 $a20230607d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe congruences of a finite lattice $ea proof-by-picture approach /$fGeorge Gra?tzer 205 $a3rd ed. 2023. 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2023] 210 4$d©2023 215 $a1 online resource (440 pages) 311 08$aPrint version: Grätzer, George The Congruences of a Finite Lattice Cham : Springer International Publishing AG,c2023 9783031290626 327 $aPart I: A Brief Introduction to Lattices -- Basic Concepts -- Special Concepts -- Congruences -- Planar Semimodular Lattices -- Part II: Some Special Techniques -- Chopped Lattices -- Boolean Triples -- Cube Extensions -- Part III: RTs -- Sectionally Complemented RT -- Minimal RT -- Semimodular RT -- Rectangular RT -- Modular RT -- Uniform RT -- Part IV: ETs -- Sectionally Complemented ET -- Semimodular ET -- Isoform ET -- Magic Wands -- Part V: Congruence Lattices of Two Related Lattices -- Sublattices -- Ideals -- Two Convex Sublattices -- Tensor Extensions -- Part VI: The Ordered Set of Principle Congruences -- The RT for Principal Congruences -- Minimal RTs -- Principal Congruence Representable Sets -- Isotone Maps -- Part VII: The Prime-Projectivity Lemma -- The Swing Lemma -- Fork Congruences -- Part VIII: The Six Congruence Properties of SPS Lattices -- Six Major Properties. 330 $aThe congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years. It features the author?s signature ?Proof-by-Picture? method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include: an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions complete proofs, an extensive bibliography and index, and over 180 illustrations additional chapters covering new results of the last seven years, increasing the size of this edition to 430 pages, 360 statements, and 262 references This text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions: ?[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. ? Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. 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. 606 $aLogic, Symbolic and mathematical 606 $aLogic, Symbolic and mathematical$xGraphic methods 606 $aTeoria dels reticles$2thub 606 $aÀlgebra$2thub 606 $aEstructures algebraiques ordenades$2thub 606 $aLògica matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aLogic, Symbolic and mathematical. 615 0$aLogic, Symbolic and mathematical$xGraphic methods. 615 7$aTeoria dels reticles 615 7$aÀlgebra 615 7$aEstructures algebraiques ordenades 615 7$aLògica matemàtica 676 $a160 700 $aGratzer$b George A.$041999 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910683352303321 996 $aThe Congruences of a Finite Lattice$91984158 997 $aUNINA