## Lattice Theory: First Concepts and Distributive LatticesLattice theory extends into virtually every area of mathematics and offers an ideal framework for understanding basic concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end-of-chapter materials and references. Both novices and experts will benefit from this treatment, which combines the techniques of an introductory text with those of a monograph. It begins with a concise development of the fundamentals of lattice theory and a detailed exploration of free lattices. The core of the text focuses upon the theory of distributive lattices. Diagrams constitute an integral part of the book, along with 500 exercises and 67 original research problems. Eight appendixes, contributed by a group of experts, complement this accessible and informative text. |

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a,b e algebraic lattice Amalgamation Property Amer atomic Balbes binary relation Boolean lattice Characterize class of lattices compact open sets concept congruence lattices congruence relation containing countable deﬁned deﬁnition denote the set Descending Chain Condition diagram direct product dual ideal E. T. Schmidt embedding equational class equivalent exercise exists Figure ﬁnite distributive lattice ﬁnite lattice ﬁrst FK(P free lattice Gratzer and E. T. Gréitzer homomorphic image iﬁ iﬂ implies inﬁnite isomorphism join-semilattice Lakser lattice and let lattice theory lattices with pseudocomplementation Lemma Let H Math mathematics maximal chain modular lattice morphism n-ary obvious one-to-one open sets partial ordering poset problems proof of Theorem Prove Q COROLLARY R-generated relative complement representation retract satisﬁes Section semilattice Show Stone algebra Stone lattice Stone space subalgebra subdirectly irreducible topological space trivial unique Verify weak partial lattice