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Record Nr. |
UNISA996495168103316 |
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Autore |
Grynkiewicz David J. <1978-> |
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Titolo |
The characterization of finite elasticities : factorization theory in Krull monoids via convex geometry / / David J. Grynkiewicz |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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9783031148699 |
9783031148682 |
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Descrizione fisica |
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1 online resource (291 pages) |
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Collana |
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Lecture notes in mathematics |
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Disciplina |
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Soggetti |
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Convex geometry |
Monoids |
Geometria convexa |
Monoides |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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