Fractional Elements and Equivalence Relations

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Covers the basics of polynomials, focusing on rings, operations, and properties.

Covers advanced topics in linear algebra, including finite fields, invertible matrices, and vector spaces.

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

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

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

Delves into functors, natural transformations, and group actions with explicit examples.

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

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

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