## Cofiniteness of local cohomology modules for principal ideals.(English)Zbl 0930.13013

In this note we show that, if an ideal $$I$$ of a Noetherian ring is principal, up to radical, then the local cohomology modules with support in $$V(I)$$ are $$I$$-cofinite.

### MSC:

 13D45 Local cohomology and commutative rings 14B15 Local cohomology and algebraic geometry 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)

### Keywords:

Ext; local cohomology modules
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