… local ring, depth ( M ⊗ R N ) = depth M + depth N − depth R , … establish a depth formula that
holds for every pair of Tate Tor-… It subsumes previous generalizations of Auslander's formula …

… Tate Tor modules. In the second part of the paper we consider a depth equality, called the
depth formula… a new sufficient condition implying the depth formula to hold for modules of finite …

… Tate homology vanishes by studying the stable homology … and vanishing of stable homology
for complexes are studied. … depth formula by proving that the vanishing of Tate homology…

… ℛ ′ is enveloping, a kind of Tate homology T o r ̂ ∗ 𝒬 ℳ of … such Tate homology functors
and relative homology functors. … Liang’s work [Tate homology of modules of finite Gorenstein …

… They provide new methods for computing Tate homology ̂ Tor and Tate cohomology ̂ …
The parallel theory of Tate homology has been treated in the same generality by Iacob [9]. While …

… will discuss about the depth formula over Gorenstein rings, … depth formula holds for nonzero
finitely generated modules M and N in case certain Gorenstein relative and Tate homology …

… In this paper, we develop a theory of Tate homology based on so-called Tate flat … a Tate flat
resolution T (see Proposition 3.4 for the existence of Tate flat resolutions), the Tate homology …

… R , ie, the depth formula holds, if M and N are Tor-independent and Tate homology Tor ˆ i
( M … Noting that the derived depth formula coincides with the depth formula for Tor-independent …

… explicit formulae for zeta elements σ2n−1 (generators of the Tannaka Lie algebra of the category
of mixed Tate motives over Z) in depths … for multiple zeta values in depths two and three. …

… of depth and width for complexes. In Section 2, we give some sufficient conditions for the
width formula to hold via vanishing of Tate … For an R-complex N, the Tate homology of M with …