Is $\mathbb R[x]/\langle (x-a)^2 \rangle $ isomorphic with some known ring ( where $a$ is a real number ) ? In particular is $\mathbb R [x] / \langle (x-1)^2 \rangle$ isomorphic with some known ring ? How many ideals do such quotient rings have ? I can determine that $\mathbb R[x]/\langle(x-a)(x-b)\rangle \cong \mathbb R \times \mathbb R$ , if $a,b$ are distinct real numbers , but having trouble if they are same ; please help . Thanks in advance .
$\Bbb EDIT$ : I am looking for a isomorphic ring which will simplify the quotient structure , loosely speaking , which will not be a quotient ring ... Thanks