Modular Arithmetic: Operations and Properties

Related lectures (29)

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

Explores fractional elements, equivalence relations, and injective mappings in commutative rings.

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

Covers commutative rings, fields, injective morphisms, characteristic, Frobenius, and binomial theorem.

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

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

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

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.