Factorization properties of quotients of polynomial and power series rings by monomial ideals

Abstract

Suppose that K is a field, S = K [ x 1 , … , x n ] or S = K [ [ x 1 , … , x n ] ] and I is a monomial ideal of S. We study factorization properties of the ring R = S / I . In particular, we present conditions equivalent to R being présimplifiable, a bounded factorization ring, a finite factorization ring or a unique factorization ring.