Ring Theory: Morphisms and Isomorphisms

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Related lectures (32)

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Algebraic Structures of Morphism Spaces

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

Module over a Ring

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

Morphism of Groups

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Ideals in Commutative Rings

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

Ring Theory: Sub-rings and Morphisms

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

Group Cohomology

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

Division Rings and Ideals

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

Idempotent Elements and Central Orthogonal

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

Localization in Algebra

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