Acta Mathematica Vietnamica
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Ideal Transforms with Respect to a Pair of Ideals
Nguyen Minh Tri
,
Tran Tuan Nam
Abstract
We introduce the ideal transform functor $D_{I,J}$ with respect to a pair of ideals $(I,J)$ which is an extension of the ideal transform functor $D_I$ 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 $\mathrm{Ass}_R (R^i D_I (N))$ and $\mathrm{Ass}R (R^i D{I, J} (M,N))$.