Localization in Algebra

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Explores modules, endomorphisms, and linear applications in algebra, including A-modules and commutative rings.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Introduces ring theory, covering definitions, examples, and subrings criteria.

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Discusses irreducible factors in rings and the properties of Noetherian rings.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Discusses Fermat's equation and Gaussian integers' properties.