Symmetric inverse semigroups / Stephen Lipscomb.

Format:

Book

Author/Creator:

Lipscomb, Stephen, 1944- author.

Series:

Mathematical surveys and monographs ; no. 46.

Mathematical surveys and monographs, 0076-5376 ; volume 46

Language:

English

Subjects (All):

Inverse semigroups.

Physical Description:

1 online resource (187 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1996]

Language Note:

English

Summary:

With over 60 figures, tables, and diagrams, this text is both an intuitive introduction to and a rigorous study of finite symmetric inverse semigroups. The book presents much of the material on the theory of finite symmetric inverse semigroups, unifying the classical finite symmetric group theory with its semigroup analogue. A comment section at the end of each chapter provides new historical perspective. New proofs, new theorems and the use of multiple figures, tables, and diagrams to present complex ideas make this book current and highly readable.

Contents:

""Contents""; ""Preface""; ""Introduction""; ""Chapter 1. Decomposing Charts""; ""Â1 Paths""; ""Â2 Building Charts from Paths""; ""Â3 Decomposing Charts into Paths""; ""Â4 Comments""; ""Chapter 2. Basic Observations""; ""Â5 Idempotents, Nilpotents, Inverses, Conjugacy""; ""Â6 Index and Period of a Chart""; ""Â7 Cyclic Subsemigroups of C[sub(n)]""; ""Â8 Comments""; ""Chapter 3. Commuting Charts""; ""Â9 Examples""; ""Â10 Characterization of Commuting Charts""; ""Â11 Comments""; ""Chapter 4. Centralizers of Permutations""; ""Â12 Examples of Centralizers""

""Â13 Centralizers as Directs Products""""Â14 Centralizers and Wreath Products""; ""Â15 Comments""; ""Chapter 5. Centralizers of Charts""; ""Â16 General Case""; ""Â17 Nilpotent Case: An Example""; ""Â18 Nilpotent Case: The Wreath Product""; ""Â19 The Quotient Semigroup""; ""Â20 Imbedding C([sub(n)]) into the Quotient Semigroup""; ""Â21 Calculations""; ""Â22 Orders of Centralizers in C[sub(n)]""; ""Â23 Comments""; ""Chapter 6. Alternating Semigroups""; ""Â24 Even Charts""; ""Â25 Members of A[sup(c)][sub(n)]""; ""Â26 Generators of Alternating Semigroups""; ""Â27 Comments""

""Chapter 9. Presentations of Symmetric Inverse Semigroups""""Â42 Review: Free Algebras, Presentations, Constructions""; ""Â43 Technical Lemma""; ""Â44 Inductive Lemma""; ""Â45 Comments""; ""Chapter 10. Presentations of Alternating Semigroups""; ""Â46 Defining Relations""; ""Â47 A[sup(c)][sub(n)] Technical Lemma""; ""Â48 A[sup(c)][sub(n)] Inductive Lemma""; ""Â49 Comments""; ""Chapter 11. Decomposing Partial Transformations""; ""Â50 Semigroup Hierarchy""; ""Â51 Path Notation for Partial Transformations""; ""Â52 Cilia and Cells of Partial Transformations""

""Â53 Idempotents and Nilpotents""""Â54 Multiplication of Partial Transformations""; ""Â55 Cyclic Semigroups of Partial Transformations""; ""Â56 Comments""; ""Chapter 12. Commuting Partial Transformations""; ""Â57 Examples""; ""Â58 Mapping Initial Segments and Cells""; ""Â59 Orders of Centrahzers of Idempotents""; ""Â60 Howie's Theorem""; ""Â61 Comments""; ""Chapter 13. Centrahzers, Conjugacy, Reconstruction""; ""Â62 Centrahzers""; ""Â63 Conjugacy in C[sub(n)]""; ""Â64 Conjugacy in PT[sub(n)]""; ""Â65 S[sub(n)]-normal Semigroups in PT[sub(n)]""; ""Â66 Graph Reconstruction""

""Â67 Isomorphic Categories of Graphs and Semigroup Extensions""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 155-162) and index.

Description based on print version record.

ISBN:

1-4704-1277-2