ExERCISE 3.6.34. Assume R is a commutative ring and :RA is a homomorphism of rings such that the image of is a subring of the center of A. Let aA and :R[x]A the evaluation map defined by xa. Let R[a] denote the image of . Show that R[a] is the smallest subring of A containing (R) and a. Show that R[a] is commutative. ExERCISE 3.6.34. Assume R is a commutative ring and :RA is a homomorphism of rings such that the image of is a subring of the center of A. Let aA and :R[x]A the evaluation map defined by xa. Let R[a] denote the image of . Show that R[a] is the smallest subring of A containing (R) and a. Show that R[a] is commutative