Homological methods in commutative algebra / Andrea Ferretti

Von:

Ferretti, Andrea, 1981- [VerfasserIn]

Resource type: Ressourcentyp: BuchBuchSprache: Englisch Reihen: Graduate studies in mathematics ; 234Verlag: Providence, Rhode Island : American Mathematical Society, [2023]Copyright-Datum: © 2023Beschreibung: xviii, 411 Seiten : IllustrationenISBN:

9781470471286
9781470474362

Schlagwörter: Andere physische Formen: 9781470474355. | Erscheint auch als: Homological methods in commutative algebra. Online-Ausgabe Providence, Rhode Island : American Mathematical Society, 2023. 1 online resourceMSC: MSC: 13-01 | 13D02 | 13D07 | 13D45 | 13H10LOC-Klassifikation:

QA251.3

Zusammenfassung: This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author’s book, Commutative Algebra (Graduate Studies in Mathematics, Volume 233). The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included. The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections. Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.PPN: PPN: 185298581X

Exemplare ( 1 )

Exemplare
Medientyp	Heimatbibliothek	Standort	Signatur	Status	Fälligkeitsdatum	Barcode	Vormerkungen
Freihandbestand ausleihbar	Fachbibliothek Mathematik	Bibliothek / frei aufgestellt	Algebr. / Fer	Verfügbar		36530565090

Anzahl Vormerkungen: 0