Complete intersection flat dimension and the intersection theorem

چکیده مقاله

Any finitely generated module M over a local ring R is endowed with a
complete intersection dimension CI-dimR M and a Gorenstein dimension G-dimR M . The
Gorenstein dimension can be extended to all modules over the ring R. This paper presents
a similar extension for the complete intersection dimension, and mentions the relation
between this dimension and the Gorenstein flat dimension. In addition, we show that in
the intersection theorem, the flat dimension can be replaced by the complete intersection
flat dimension.