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The book explores the Morita Theorems, presenting simplified proofs that link ring theory and category theory. It discusses the equivalence of categories mod-A and mod-B for rings A and B, showcasing the efficiency of Morita's organization of ideas, which leads to the classical Wedderburn-Artin theorem. Additionally, it introduces new theorems within ring theory, particularly in Chapter 4, which focuses on projective modules and lays the groundwork for a comprehensive theory of simple Noetherian rings. The text is rich with insights and connections in algebra.
Buchkauf
Algebra, Carl Faith
- Sprache
- Erscheinungsdatum
- 2012
- product-detail.submit-box.info.binding
- (Paperback)
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- Titel
- Algebra
- Untertitel
- Rings, Modules and Categories I
- Sprache
- Englisch
- Autor*innen
- Carl Faith
- Erscheinungsdatum
- 2012
- Einband
- Paperback
- Seitenzahl
- 592
- ISBN13
- 9783642806360
- Kategorie
- Mathematik
- Beschreibung
- The book explores the Morita Theorems, presenting simplified proofs that link ring theory and category theory. It discusses the equivalence of categories mod-A and mod-B for rings A and B, showcasing the efficiency of Morita's organization of ideas, which leads to the classical Wedderburn-Artin theorem. Additionally, it introduces new theorems within ring theory, particularly in Chapter 4, which focuses on projective modules and lays the groundwork for a comprehensive theory of simple Noetherian rings. The text is rich with insights and connections in algebra.