Abstract
Let A be a commutative ring with identity and the ring of formal power series in n variables. In this paper, we consider the SFT-property on A and its relation with
. Then, we see when the minimal prime ideals of
are extended from those of A. We discuss the notion of nicely-contractible ideals in
and its relation with the SFT-property. We apply our results to the
ideals and the
ideals of
.