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Bull. Korean Math. Soc. 2013; 50(6): 1855-1861

Printed November 1, 2013

https://doi.org/10.4134/BKMS.2013.50.6.1855

Copyright © The Korean Mathematical Society.

On the weak Artinianness and minimax generalized local cohomology modules

Yan Gu

Soochow University

Abstract

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Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$, $M$ and $N$ two $R$-modules. We characterize the least integer $i$ such that $H^i_I(M,N)$ is not weakly Artinian by using the notion of weakly filter regular sequences. Also, a local-global principle for minimax generalized local cohomology modules is shown and the result generalizes the corresponding result for local cohomology modules.

Keywords: generalized local cohomology modules, weak Artinianness, minimax module

MSC numbers: 13D45, 13E10

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