Lectures related to Ring Theory: Sub-rings and Morphisms

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

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

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

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

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

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.

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

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

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Explores operations on ideals and structure theorems in commutative rings.

Explores F-G sheaf morphisms, sheafification, and localization in ring theory.