Commutative Algebra Notes Introduction to Commutative Algebra Atiyah & Macdonald

نویسنده

  • Adam Boocher
چکیده

and we call A the zero ring denoted by 0. A ring homomorphism is a mapping f of a ring A into a ring B such that for all x, y ∈ A, f(x + y) = f(x) + f(y), f(xy) = f(x)f(y) and f(1) = 1. The usual properties of ring homomorphisms can be proven from these facts. A subset S of A is a subring of A if S is closed under addition and multiplication and contains the identity element of A. The identity inclusion map f : S → A is then a ring homomorphism. The composition of two homomorphisms is a homomorphism.

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تاریخ انتشار 2007