Integral Closures: Eisenstein Primes

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Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

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

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.