Abstract:
This paper aims to generalize results on single variable polynomial rings over commutative rings with zerodivisors to the case of polynomial rings in arbitrarily many variables. Given a commutative ring R, we give necessary and sufficient conditions for the ring of polynomials with coefficients in R in arbitrarily many variables to be a PVMR and Krull ring. In answering these questions, we make use of the t and v operations on ideals as a means of characterizing these rings. We also give conjectures on necessary and
sufficient conditions for an arbitrary polynomial ring to be a Dedekind ring, a UFR, and integrally closed.