Quotient module

Consider the polynomial ring, with real coefficients, and the -module A=\R[X], . Consider the submodule :B = (X^2+1) \R[X] of , that is, the submodule of all polynomials divisible by . It follows that the equivalence relation determined by this module will be : if and only if and give the same remainder when divided by . Therefore, in the quotient module , is the same as 0; so one can view as obtained from by setting . This quotient module is isomorphic to the complex numbers, viewed as a module over the real numbers ==See also==