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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a₁ Algebra Universalis algebraic lattice arguesian atoms b₁ binary relation boolean algebra boolean lattice bounded lattice chopped lattice compact complemented lattice complete lattice con(a congruence lattice congruence relation congruence-preserving extension Corollary define Definition denote direct product dual duality dually E. T. Schmidt elements embedding equivalent Exercise exists finite lattice free lattice free product Freek geometric lattice geometry Grätzer and E. T. hence holds homomorphism id(a identity implies isomorphic join-irreducible join-semilattice Jónsson Lakser lattice and let lattice theory lattice with zero Lemma Math maximal chain mod ẞ modular lattice nonempty obvious open sets P₁ partial lattice prime ideal proof of Theorem Prove pseudocomplemented relatively complemented representation result satisfying sectionally complemented semilattice semimodular lattices Show Skel Spec Stone algebra subdirectly irreducible sublattice subset topological universal algebra variety of lattices verify Wehrung