Abstract
LetĪ be a mulitiplicatively closed set of nonzero idcals of a Noetherian ring R and for an ideal I of R let IĪ=āŖ{I:G;GāĪlcub; Then IĪ is an ideal in R and it is shown that if P is prime divisor of IĪ, then P is a prime divisor of IG:Gā² for all G,Gā² In $GgR;. Alao, for a given filtration is a filtration on R and when Ļ is Noetherian several necessary and sufficient conditions are given for Ļ and ĻĪ to give linearly equivalent ideal topologies on R .
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