The reduction ring property is hereditary (Q809150)

Roughly speaking, a reduction ring is one that allows Gröbner basis constructions (the exact definition would take much place). It is stated that if R is a reduction ring, then the ring \(R^ n\) and, under additional conditions on R, the ring R/A are also reduction rings, where \(A\subseteq R\) is a finitely generated ideal. Proofs are outlined.