Algebra. Rings, Modules and Categories I

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.