SFT stability via power series extension over Prufer domains

Abstract

A ring D is called an SFT ring if for each ideal I of D, there exist a natural number k and a finitely generated ideal J subset of I such that a(k) is an element of J for each a is an element of I. We show that the power series ring D[[x(1),..., x(n)]] over an SFT Prufer domain D is again an SFT ring even if D is infinite-dimensional. From this, it follows that every ideal-adic completion of D is also an SFT ring. We also show that D[[x(1),..., x(n)]](D\(0)) is an n-dimensional regular ring.