… , for commutative rings in terms of the vanishing of Tor. This has led to the notion of Tor-persistent
rings. Our main result shows that the class of Tor-persistent local rings is closed under …

… We use that information to construct and define the Tor functor, the key element to our …
isomorphism between self Tor on the (p − 1)th syzygy module and the 1st homology module of a …

… Here is an example showing that in the general setting of Theorem 2.7, vanishing of TorR …
Jorgensen, Vanishing of Tate homology and depth formulas over local rings, J. Pure Appl. …

… modules can be implemented in Python. To redirect Python’s networking API over Tor’s SOCKS
port, we extended the SocksiPy module … 2,698 exit relays vanished after being part of the …

… As in [82] we define the Ext-depth and the Tor-codepth of an R-module M with … R-module
\(\hat{M}^{\mathfrak a}/M\) is also finitely generated. Hence by Nakayama’s lemma it vanishes …

… We prove rigidity type results on the vanishing of stable Ext and Tor for modules … Tor for
finitely generated modules over unramified regular local rings was resolved by Auslander himself…

… Secondly, we examine the problem on the self-duality. As is well-… We determine the class of
noetherian rings for which the self-duality … the width) by the vanishing of Tor modules, and the …

0. Introduction. Let E be a modular elliptic curve defined over with the conductor N, and let XE
xE, which is by definition a projective smooth surface over. Let CHo (X) be the Chow group …

… of modules under certain conditions on the vanishing of Tor. … of two modules with three
consecutive vanishing Tors. In this … that if sufficiently many Tors vanish for two modules M, N and …

… of the theory of D-rings that is as selfcontained as possible. This need has … in terms of the
vanishing of the functor Ext (Q, •). … Note that Tor(Q, A) = 0, since Q is a flat R-module. Dualizing …