The classical Lie algebras

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Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Explores Lie algebra, Casimirs, and Poincaré in SO(3) transformations.

Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.

Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.

Covers Lie theorems, group algebra, Ado's theorem, and spacetime symmetries.

Covers Lie Algebra, focusing on vector space and multiplication law.

Explores the significance of the Jacobi identity in Lie algebra and its impact on linear vector spaces.

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

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

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

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