The congruences of a finite lattice : a "proof-by-picture" approach
著者
書誌事項
The congruences of a finite lattice : a "proof-by-picture" approach
Birkhäuser , Springer, c2016
2nd ed
大学図書館所蔵 全3件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 323-336) and index
内容説明・目次
内容説明
This is a self-contained exposition by one of the leading experts in lattice theory, George Gratzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method.
Key features:
* Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions
* Contains complete proofs, an extensive bibliography and index, and over 140 illustrations
* This new edition includes two new parts on Planar Semimodular Lattices and The Order of Principle Congruences, covering the research of the last 10 years
The book is appropriate for a one-semester graduate course in lattice theory, and it is a practical reference for researchers studying lattices.
Reviews of the first edition:
"There exist a lot of interesting results in this area of lattice theory, and some of them are presented in this book. [This] monograph...is an exceptional work in lattice theory, like all the contributions by this author. ... The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. Moreover, the author provides a series of companion lectures which help the reader to approach the Proof-by-Picture sections." (Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007)
"The book is self-contained, with many detailed proofs presented that can be followed step-by-step. [I]n addition to giving the full formal details of the proofs, the author chooses a somehow more pedagogical way that he calls Proof-by-Picture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." -Mathematical Reviews
目次
I: A Brief Introduction to Lattices.- Basic Concepts.- Special Concepts.- Congruences.- Planar Semimodular Lattices.- II: Some Special Techniques.- Chopped Lattices.- Boolean Triples.- Cubic Extensions.- III: Congruence Lattices of Finite Lattices.- The Dilworth Theorem.- Minimal Representations.- Semimodular Lattices.- Rectangular Lattices.- Modular Lattices.- Uniform Lattices.- IV: Congruence Lattices and Lattice Extensions.- Sectionally Complemented Lattices.- Semimodular Lattices.- Isoform Lattices.- The Congruence Lattice and the Automorphism Group.- Magic Wands.- V: Congruence Lattices of Two Related Lattices.- Sublattices.- Ideals.- Tensor Extensions.- VI The Ordered Set of Principal Congruences.- Representation Theorems.- Isotone Maps.- VII: Congruence Structure.- Prime Intervals and Congruences.- Some Applications of the Swing Lemma.
「Nielsen BookData」 より