Some Results on Generalized Local Cohomology Modules

Abstract

Let R be a commutative Noetherian ring with nonzero identity, 𝔞 an ideal of R, M a finite R–module, X an arbitrary R–module, and n a non-negative integer. Here, we show that, in the Serre subcategories of the category of R–modules, how the generalized local cohomology modules, the ordinary local cohomology modules, and the extension modules behave similarly at the initial points i ≤ n. We conclude with some Artinianness and cofiniteness results for , and some finiteness results for and .

Key Words:

• Generalized local cohomology modules
• Serre subcategories

2010 Mathematics Subject Classification:

• 13D07
• 13D45

ACKNOWLEDGMENTS

The authors would like to thank the referee for the comments on the manuscript.

The second author would like to dedicate this article to the dear and loving memory of his late father who battled cancer and lost the fight in December 2013.

Notes

Communicated by E. Kirkman.