Buch, Englisch, 282 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 452 g
Reihe: Lecture Notes in Mathematics
Factorization Theory in Krull Monoids via Convex Geometry
Buch, Englisch, 282 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 452 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-031-14868-2
Verlag: Springer International Publishing
This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids.
This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
- 1. Introduction. - 2. Preliminaries and General Notation. - 3. Asymptotically Filtered Sequences, Encasement and Boundedness. - 4. Elementary Atoms, Positive Bases and Reay Systems. - 5. Oriented Reay Systems. - 6. Virtual Reay Systems. - 7. Finitary Sets. - 8. Factorization Theory.