x Example: IfR is a ring, then rix denotes the set of polynomials with coefficients in R. We shall not give a formal definition of this set, but it can be thought of as: rx= a0+ajx+ a2x +…+anx叫n∈Z,a∈R} a Multiplication and addition are defined in the usual manner: if f(x)=∑a, c and g(x)=∑ bx' then max( n, m) f(x)+g(x)=∑(+b)xf(x)*g(x)=∑∑(ab,)x k=0计+j=k One then has to check that these operations define a ring The ring is called polynomial ring. Example: If R is a ring, then R[x] denotes the set of polynomials with coefficients in R. We shall not give a formal definition of this set, but it can be thought of as: R[x] = {a0 + a1x + a2x 2 + …+ anx n |nZ+ , aiR}.  Multiplication and addition are defined in the usual manner; if   = = = = m i i i n i i i f x a x and g x b x 0 0 ( ) ( ) then = + = + max{ , } 0 ( ) ( ) ( ) n m i i i i f x g x a b x   + = + =  = n m k k i j i j k f x g x a b x 0 ( ) ( ) ( ) One then has to check that these operations define a ring. The ring is called polynomial ring