Notes on Algebra a Little Bit of Homological Algebra
نویسنده
چکیده
Definition 1.1. Suppose that R is a commutative ring (possibly a field) and that A, B and C are R-modules. A function f : A× B → C is bilinear if • f (a1 + a2, b) = f (a1, b) + f (a1, b), • f (a, b1 + b2) = f (a, b1) + f (a, b2), and • f (ra, b) = f (a, rb) = r f (a.b). 1.2. The most basic examples of bilinear functions are the functions R×R→ R given by homogeneous quadratic polynomials of degree 2 (also known as a quadratic forms). For example, the function f (x, y) = xy is a bilinear function from R×R→ R. If F is a field, and V = F n then the dot product gives an example of a bilinear function f : V × V → F .
منابع مشابه
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تاریخ انتشار 2005