THE ARTINIANESS AND -STABLE OF LOCAL HOMOLOGY MODULE WITH RESPECT TO A PAIR OF IDEALS
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Abstract
The concept of -stable modules was defined by Tran Tuan Nam (Tran, 2013), and the author used it to study the representation of local homology modules. In this paper, we will introduce the concept of -stable modules, which is an extension of the -stable modules. We study the -stable for local homology modules with respect to a pair of ideals, these modules have been studied by Tran and Do (2020). We show some basic properties of -stable modules and use them to study the artinianess of local homology modules with respect to a pair of ideals. Moreover, we also examine the relationship between the artinianess, -stable, and the varnishing of local homology module with respect to a pair of ideals.
Keywords
artinian module, -stable module, local homology
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References
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