Algebraic Structures of Morphism Spaces

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Related lectures (32)

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Ring Theory: Sub-rings and Morphisms

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

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Integrity in Algebra

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

Ring of Polynomials: Coefficients and Multiplication

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

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Homomorphisms and Projective Resolutions

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Rings and Modules: Color Codes and Homological Algebra

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Congruence Relations in Rings

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

Isomorphism of Groups

Covers bijections between automorphisms and equivariant bijections in group isomorphisms.