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Acta Mathematica Vietnamica

Ideal Transforms with Respect to a Pair of Ideals

Nguyen Minh Tri , icon-email Tran Tuan Nam

Abstract

We introduce the ideal transform functor DI,J with respect to a pair of ideals (I,J) which is an extension of the ideal transform functor DI of Brodmann. Some equivalent conditions on the exactness of the ideal transform functor will be shown in the paper. We also study the finiteness of the sets AssR(RiDI(N)) and $\mathrm{Ass}R (R^i D{I, J} (M,N))$.