Depth formula via complete intersection flat dimension

چکیده مقاله

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 $i\ge 1$.