The ring A[X,Y;λ] and the SFT property

Abstract

Let A be a ring and λ : R ≥ 0 → R ≥ 0 be an increasing nonzero function. In this paper, we show that if A is a Noetherian ring with characteristic n ≠ 0 and lim k → + ∞ λ ( k + 1 ) λ ( k ) = + ∞ , then A [ X , Y ; λ ] is an SFT ring. This result allows us to construct a nonNoetherian SFT ring which has some Noetherian completion. Also, we use the composite ring extension to construct many examples of such rings. Many examples are provided.