In the paper (2.11) the authors show that if k∗ is a separable algebraic extension of k and x1,x2,…,xn are indeterminates over k∗ and a normal one dimensional ring A with k⊂A⊂k∗[x1,x2,…,xn] then A has the form k′[t] where k′ is the algebraic closer of k in A.

The above is a very strict sufficient condition to ensure the polynomial property. Is there a general answer to the question:

Q. When a ring R is a polynomial ring over a field?

**Answer**

**Attribution***Source : Link , Question Author : mukhujje , Answer Author : Community*