Ring Theory: Sub-rings and Morphisms

Related lectures (33)

Explores the properties of commutative rings and integral domains in algebra.

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Covers non-degenerate integral quadratic lattices and adèles, including their properties and definitions.

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Covers the ring of polynomials, focusing on coefficients and multiplication.

Explores the construction of quotient rings and the properties of well-defined operations within rings.

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

Introduces ring theory, covering definitions, examples, and subrings criteria.

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

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Discusses irreducible factors in rings and the properties of Noetherian rings.

Explores modules over a ring, injective morphisms, isomorphisms, and canonical groups.

Discusses Fermat's equation and Gaussian integers' properties.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Page 1 of 2