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arXiv · 1008.1637

Depth formula via complete intersection flat dimension

Parviz Sahandi·Tirdad Sharif·Siamak Yassemi
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Abstract

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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Parviz Sahandi, Tirdad Sharif, Siamak Yassemi. 2010-08-10. Depth formula via complete intersection flat dimension. https://arxiv.org/abs/1008.1637

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