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020 _a9783034800181
_99783034800181
024 7 _a10.1007/9783034800181
_2doi
035 _avtls000345233
039 9 _a201509030410
_bVLOAD
_c201405050318
_dVLOAD
_y201402061331
_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA241-247.5
100 1 _aGrätzer, George.
_eautor
_9304276
245 1 0 _aLattice Theory: Foundation /
_cby George Grätzer.
264 1 _aBasel :
_bSpringer Basel,
_c2011.
300 _axxIx, 613 páginas
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
500 _aSpringer eBooks
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)
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9783034800174
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-0348-0018-1
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999 _c292854
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