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001 978-3-0348-0018-1
003 DE-He213
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007 cr nn 008mamaa
008 110214s2011 sz | s |||| 0|eng d
020 _a9783034800181
_9978-3-0348-0018-1
024 7 _a10.1007/978-3-0348-0018-1
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aGrätzer, George.
_eauthor.
245 1 0 _aLattice Theory: Foundation
_h[electronic resource] /
_cby George Grätzer.
264 1 _aBasel :
_bSpringer Basel,
_c2011.
300 _aXXIX, 613p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Introduction -- Glossary of Notation -- I First Concepts -- 1 Two Definitions of Lattices -- 2 How to Describe Lattices -- 3 Some Basic Concepts -- 4 Terms, Identities, and Inequalities -- 5 Free Lattices -- 6 Special Elements -- II Distributive Lattices -- 1 Characterization and Representation Theorems -- 2 Terms and Freeness -- 3 Congruence Relations -- 4 Boolean Algebras -- 5 Topological Representation -- 6 Pseudocomplementation -- III Congruences -- 1 Congruence Spreading -- 2 Distributive, Standard, and Neutral Elements -- 3 Distributive, Standard, and Neutral Ideals -- 4 Structure Theorems -- IV Lattice Constructions -- 1 Adding an Element -- 2 Gluing -- 3 Chopped Lattices -- 4 Constructing Lattices with Given Congruence Lattices -- 5 Boolean Triples -- V Modular and Semimodular Lattices -- 1 Modular Lattices -- 2 Semimodular Lattices -- 3 Geometric Lattices -- 4 Partition Lattices -- 5 Complemented Modular Lattices -- VI Varieties of Lattices -- 1 Characterizations of Varieties 397 -- 2 The Lattice of Varieties of Lattices -- 3 Finding Equational Bases -- 4 The Amalgamation Property -- VII Free Products -- 1 Free Products of Lattices -- 2 The Structure of Free Lattices -- 3 Reduced Free Products -- 4 Hopfian Lattices -- Afterword -- Bibliography.
520 _aThis book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Over 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Garrett Birkhoff (Bulletin of the American Mathematical Society) “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” (Mathematical Reviews)
650 0 _aMathematics.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034800174
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0018-1
912 _aZDB-2-SMA
999 _c106580
_d106580