Depth formula via complete intersection flat dimension

Details Depth formula via complete intersection flat dimension Depth formula via complete intersection flat dimension

2010-08-10

arxiv.org/abs/1008.1637v1

Mathematics

Commutative Algebra

10 pages, to appear in comm. Algebra

Scientific paper

We prove the depth formula, for homologically bounded complexes $X, Y$
provided that the complete intersection flat dimension of $X$ is finite and
$\sup(X\utp_RY)<\infty$. In particular, let $M$ and $N$ are two $R$-modules and
the complete intersection flat dimension of $M$ is finite. Then $M$ and $N$
satisfies the depth formula, provided $\Tor^R_i(M,N)=0$ for all $i\ge 1$.

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