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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