Rings with uniformly S-SFT

In this article, we examine the notion of uniformly S-SFT and study its properties. Let R be a commutative ring and S a multiplicative subset of R. A ring R is said to be uniformly S-SFT if there exists an element s in S such that for every ideal I of R, there exist a finitely generated sub-ideal J of I and a positive integer n with the property that sna ? J for all a in I. Our investigation includes proving Cohen?s Theorem for uniformly S-SFT rings and analyzing the behavior of uniformly S-SFT property under various ring operations like Nagata?s idealization and amalgamation of algebras.