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Related lectures (31)

Chinese Remainder Theorem and Polynomial Rings

Covers the Chinese remainder theorem, polynomial rings, and Euclidean domains among other topics.

Algebra Review: Rings, Fields, and Groups

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Schur's Lemma and Representations

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

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Ideals and PPCM

Covers the concept of ideals in polynomial rings and their properties.

Principle of Superposition in Differential Equations

Explores the principle of superposition in differential equations and the fundamental theorem of algebra.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Rings and Fields: Principal Ideals and Ring Homomorphisms

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Algebraic Geometry: Rings and Bodies

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

Polynomial Rings and Irreducibility Criteria

Covers polynomial rings, irreducibility criteria, and algebraic structures in fields.

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