Algebraic Extensions

Related lectures (32)

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Explores purely inseparable decompositions, Galois property, and algebraic closures.

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

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

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

Explores transcendence degree in algebraic fields and classical analytic functions.

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

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Covers the basics of finite fields, including arithmetic operations and properties.