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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.
Nákup knihy
Algebra, Carl Faith
- Jazyk
- Rok vydania
- 2012
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- Titul
- Algebra
- Podtitul
- Rings, Modules and Categories I
- Jazyk
- anglicky
- Autori
- Carl Faith
- Vydavateľ
- Springer Berlin Heidelberg
- Rok vydania
- 2012
- Väzba
- mäkká
- Počet strán
- 592
- ISBN13
- 9783642806360
- Kategórie
- Matematika
- Anotácia
- 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.