# Math Help - Let R=C[x1...xn]/I be a quotient of a polynomial ring overC, and let M be a maximal

1. ## Let R=C[x1...xn]/I be a quotient of a polynomial ring overC, and let M be a maximal

Let R=C[x1...xn]/I be a quotient of a polynomial ring overC, and let M be a maximal ideal of R. Prove that R/M isomorphic to C

2. Originally Posted by dabien
Let R=C[x1...xn]/I be a quotient of a polynomial ring overC, and let M be a maximal ideal of R. Prove that R/M isomorphic to C

R/M is an extension field which is a fin. gen. algebra over C and thus it is algebraic over C (why? This is the main point here) ==> as C is algebraically closed we get at once R/M ~ C

Tonio