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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.
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Algebra. Rings, Modules and Categories I, Carl Faith
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- Language
- Released
- 1973
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- (Hardcover)
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- Title
- Algebra. Rings, Modules and Categories I
- Language
- English
- Authors
- Carl Faith
- Publisher
- Springer-Verlag
- Released
- 1973
- Format
- Hardcover
- ISBN10
- 3540055517
- ISBN13
- 9783540055518
- Category
- Mathematics
- Description
- 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.