000 03218nam a22004815i 4500
001 978-0-8176-4462-8
003 DE-He213
005 20251006084435.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780817644628
020 _a99780817644628
024 7 _a10.1007/0-8176-4462-8
_2doi
082 0 4 _a511.33
_223
100 1 _aGrätzer, George.
_eauthor.
245 1 4 _aThe Congruences of a Finite Lattice
_h[electronic resource] :
_bA Proof-by-Picture Approach /
_cby George Grätzer.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2006.
300 _aXXII, 282 p. 110 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aA Brief Introduction to Lattices -- Basic Concepts -- Special Concepts -- Congruences -- Basic Techniques -- Chopped Lattices -- Boolean Triples -- Cubic Extensions -- Representation Theorems -- The Dilworth Theorem -- Minimal Representations -- Semimodular Lattices -- Modular Lattices -- Uniform Lattices -- Extensions -- Sectionally Complemented Lattices -- Semimodular Lattices -- Isoform Lattices -- Independence Theorems -- Magic Wands -- Two Lattices -- Sublattices -- Ideals -- Tensor Extensions.
520 _aThe congruences of a lattice form the congruence lattice. In the past half-century, the study of congruence lattices has become a large and important field with a great number of interesting and deep results and many open problems. This self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presents the major results on congruence lattices of finite lattices featuring the author's signature "Proof-by-Picture" method and its conversion to transparencies. Key features: * Includes the latest findings from a pioneering researcher in the field * 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 nearly 80 open problems * Additional information provided by the author online at: http://www.maths.umanitoba.ca/homepages/gratzer.html/ The book is appropriate for a one-semester graduate course in lattice theory, yet is also designed as a practical reference for researchers studying lattices.
650 0 _aMATHEMATICS.
650 0 _aALGEBRA.
650 0 _aLOGIC, SYMBOLIC AND MATHEMATICAL.
650 0 _aNUMBER THEORY.
650 0 _aDISTRIBUTION (PROBABILITY THEORY).
650 1 4 _aMATHEMATICS.
650 2 4 _aORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES.
650 2 4 _aMATHEMATICAL LOGIC AND FOUNDATIONS.
650 2 4 _aALGEBRA.
650 2 4 _aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
650 2 4 _aNUMBER THEORY.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817632243
856 4 0 _uhttp://dx.doi.org/10.1007/0-8176-4462-8
_zVer el texto completo en las instalaciones del CICY
912 _aZDB-2-SMA
942 _2ddc
_cER
999 _c59653
_d59653