We prove some results about the finiteness of co-associated primes of generalized local homology ... more We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog’s generalized local cohomology modules.
We study basic properties of the generalized ideal transforms DI (M, N) and the set of associated... more We study basic properties of the generalized ideal transforms DI (M, N) and the set of associated primes of the modules RiDI (M, N).
International Journal of Algebra and Computation, 2014
We introduce a notion of generalized local cohomology modules with respect to a pair of ideals (I... more We introduce a notion of generalized local cohomology modules with respect to a pair of ideals (I, J) which is a generalization of the concept of local cohomology modules with respect to (I, J). We show that generalized local cohomology modules [Formula: see text] can be computed by the Čech cohomology modules. We also study the artinianness of generalized local cohomology modules [Formula: see text].
We introduce generalized local homology which is in some sense dual to generalized local cohomolo... more We introduce generalized local homology which is in some sense dual to generalized local cohomology, and study some properties of generalized local homology modules for artinian modules, such as the artinianness, noetherianness and the characterization of Width I(M) by generalized local homology. By using duality, we get back some properties of generalized local cohomology.
We prove some results about the finiteness of co-associated primes of generalized local homology ... more We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog’s generalized local cohomology modules.
We study basic properties of the generalized ideal transforms DI (M, N) and the set of associated... more We study basic properties of the generalized ideal transforms DI (M, N) and the set of associated primes of the modules RiDI (M, N).
International Journal of Algebra and Computation, 2014
We introduce a notion of generalized local cohomology modules with respect to a pair of ideals (I... more We introduce a notion of generalized local cohomology modules with respect to a pair of ideals (I, J) which is a generalization of the concept of local cohomology modules with respect to (I, J). We show that generalized local cohomology modules [Formula: see text] can be computed by the Čech cohomology modules. We also study the artinianness of generalized local cohomology modules [Formula: see text].
We introduce generalized local homology which is in some sense dual to generalized local cohomolo... more We introduce generalized local homology which is in some sense dual to generalized local cohomology, and study some properties of generalized local homology modules for artinian modules, such as the artinianness, noetherianness and the characterization of Width I(M) by generalized local homology. By using duality, we get back some properties of generalized local cohomology.
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Papers by Tuan Nam Tran