Algebraic Extensions and Decomposition of Fok [x]

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Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

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

Covers the concept of the free product in group theory and how to determine monomorphisms and homomorphisms.

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.