Miklos Schweitzer 1966_8
Source:
September 29, 2008
algebrapolynomialfunctionRing Theorysuperior algebrasuperior algebra unsolved
Problem Statement
Prove that in Euclidean ring the quotient and remainder are always uniquely determined if and only if is a polynomial ring over some field and the value of the norm is a strictly monotone function of the degree of the polynomial. (To be precise, there are two trivial cases: can also be a field or the null ring.)
E. Fried