Varieties of LatticesThe study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work. |
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
General Results | 13 |
Modular Varieties | 46 |
Nonmodular Varieties | 77 |
Copyright | |
3 other sections not shown
Other editions - View all
Tutorials in Mathematical Biosciences IV: Evolution and Ecology Avner Friedman No preview available - 2007 |
Séminaire de Probabilités XL Catherine Donati-Martin,Michel Émery,Alain Rouault,Christophe Stricker No preview available - 2007 |
Common terms and phrases
algebras Amal(V amalgamation property Applications Arguesian assume atoms bounded Chapter choose Clearly complemented complete Con(A condition congruence distributive variety Consequently consider construct contains contradiction Conversely Corollary covers define definition denote Desargues distinct distributive lattice dual dually element elementary embedding epimorphism equational equivalent excludes exists extension fact fails Figure filter finite lattice finitely based follows free lattice Geometry give given hence holds homomorphic image identity implies includes isomorphic join irreducible join-cover Jónsson lattice varieties least Lemma length meet minimal modular lattice n-frame nontrivial Note Observe obtain points prime quotient Proceedings projective projective space PROOF prove quotient relations relative representation result Rose satisfies semidistributive sequence similarly splitting lattice steps subdirectly irreducible sublattice subset subvarieties Suppose Theorem Theory trivial unique whence
Bibliographic information
| Title | Varieties of Lattices Lecture Notes in Mathematics |
| Authors | Peter Jipsen, Henry Rose |
| Edition | illustrated |
| Publisher | Springer Berlin Heidelberg, 1992 |
| Original from | the University of California |
| Digitized | Jun 4, 2011 |
| ISBN | 3540563148, 9783540563143 |
| Length | 166 pages |
| Subjects | › › Mathematics / Algebra / General |
| Export Citation | BiBTeX EndNote RefMan |