Classes of Good Noetherian Rings
Seiten
2023
|
1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-22291-7 (ISBN)
Springer International Publishing (Verlag)
978-3-031-22291-7 (ISBN)
This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini’s Theorem, and Cohen factorizations.
This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini's Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescu's Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.
This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini's Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescu's Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.
1. Fibres of Noetherian Rings.- 2. Nagata Rings and Reduced Morphisms.- 3. Excellent Rings and Regular Morphisms.- 4. Localization and Lifting Theorems.- 5. Structure of Regular Morphisms.- 6. Further Results on Classes of Good Rings.
"The book wraps up with an extensive bibliography, covering not just references, but also encompassing monographs, textbooks, and research papers that share thematic connections with the subject matter explored in the book and offering a historical perspective on the theory's development. The book is recommended for PhD students and researchers in commutative algebra, algebraic and arithmetic geometry, and number theory." (Jebrel M. Habeb, zbMATH 1528.13001, 2024)
| Erscheinungsdatum | 30.03.2023 |
|---|---|
| Reihe/Serie | Frontiers in Mathematics |
| Zusatzinfo | XIV, 480 p. 1 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 168 x 240 mm |
| Gewicht | 782 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Schlagworte | Algebraic Geometry • Algebraic Structures • Bertini's Theorem • Cohen Factorizations • Commutative algebra • Nagata Rings • Neron Desingularization • Noetherian Local Rings • Noetherian rings • Popescu's Theorem • Regular Morphism Algebraic Geometry • Resolution of Singularities • Rings Formal Fibres |
| ISBN-10 | 3-031-22291-1 / 3031222911 |
| ISBN-13 | 978-3-031-22291-7 / 9783031222917 |
| Zustand | Neuware |
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Buch | Softcover (2022)
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