Epsilonization: Algebra Homomorphisms and Derivation Numbers

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Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

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

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Covers the construction and universal properties of pushouts in group theory.

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

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

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.