Notes on Modules and Algebras
نویسنده
چکیده
For objects A and B belonging to a category C we denote by C(A,B) the set of all morphisms from A to B in C and, for any f ∈ C(A,B), the objects A and B are called, respectively, the domain and codomain of f . For example, if A and B are abelian groups, and we denote by U(A) and U(B) the underlying sets of A and B, then Ab(A,B) is the set of all group homomorphisms having domain A and codomain B, while Set(U(A), U(B)) is the set of all functions from A to B, where the group structure is ignored. Whenever it is understood that A and B are objects in some category C then by a morphism from A to B we shall always mean a morphism from A to B in the category C. For example if A and B are rings, a morphism f : A → B is a ring homomorphism, not just a homomorphism of underlying additive abelian groups or multiplicative monoids, or a function between underlying sets.
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