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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 limk→+∞λ(k+1)λ(k)=+∞, then AX,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.
Dabbabi et al. (Wed,) studied this question.
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