Lattice Theory: FoundationThis 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. Almost 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.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews |
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algebras apply associated assume atoms block boolean algebra boolean lattice bounded called characterization closed compact concept conclude congruence lattice congruence relation construction contains converse Corollary covers define Definition denote described direct distributive lattice dual duality elements embedding equivalent example Exercise exists extension Figure Find finite lattice free lattice free product function geometry given Grätzer hence holds homomorphism id(a ideal identity implies infinite interval introduced isomorphic join lattice and let lattice L lattice theory Lemma length Let L Math maximal meet modular lattice Note Observe obtain obvious operations pair points prime ideal problem projective Proof proper properties Prove representation represented result ring satisfying semimodular sequence Show Similarly space statement Stone sublattice subset Theorem topological unique variety verify zero