Algebraic Structures of Morphism Spaces

This lecture covers the algebraic structures of morphism spaces, including the notation for sets of morphisms and automorphisms of modules, stability properties, and bijective morphisms. It also discusses the natural group structure of Hom-modules and the additional module structure when the ring is commutative. The lecture further explores endomorphisms of modules, the concept of a field, and the definition of a body. It concludes with propositions and lemmas related to injective ring homomorphisms and non-zero subrings of a field.