The characterization of finite elasticities : factorization theory in Krull monoids via convex geometry / David J. Grynkiewicz.

Author
Grynkiewicz, David J., 1978- [Browse]
Format
Book
Language
English
Published/​Created
  • Cham, Switzerland : Springer, [2022]
  • ©2022
Description
1 online resource (291 pages)

Details

Subject(s)
Series
Bibliographic references
Includes bibliographical references and index.
Source of description
Description based on print version record.
Contents
  • Intro
  • Preface
  • Contents
  • 1 Introduction
  • 1.1 Convex Geometry
  • 1.2 Krull Domains, Transfer Krull Monoids and Factorization
  • 1.3 Zero-Sum Sequences
  • 1.4 Overview of Main Results
  • 2 Preliminaries and General Notation
  • 2.1 Convex Geometry
  • 2.2 Lattices and Partially Ordered Sets
  • 2.3 Sequences and Rational Sequences
  • 2.4 Arithmetic Invariants for Transfer Krull Monoids
  • 2.5 Asymptotic Notation
  • 3 Asymptotically Filtered Sequences, Encasement and Boundedness
  • 3.1 Asymptotically Filtered Sequences
  • 3.2 Encasement and Boundedness
  • 4 Elementary Atoms, Positive Bases and Reay Systems
  • 4.1 Basic Non-degeneracy Characterizations
  • 4.2 Elementary Atoms and Positive Bases
  • 4.3 Reay Systems
  • 4.4 -Filtered Sequences, Minimal Encasement and Reay Systems
  • 5 Oriented Reay Systems
  • 6 Virtual Reay Systems
  • 7 Finitary Sets
  • 7.1 Core Definitions and Properties
  • 7.2 Series Decompositions and Virtualizations
  • 7.3 Finiteness Properties of Finitary Sets
  • 7.4 Interchangeability and the Structure of X(G0)
  • 8 Factorization Theory
  • 8.1 Lambert Subsets and Elasticity
  • 8.2 The Structure of Atoms and Arithmetic Invariants
  • Summary
  • 8.3 Transfer Krull Monoids Over Subsets of Finitely Generated Abelian Groups
  • References
  • Index.
ISBN
9783031148699 ((electronic bk.))
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