This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...

We construct hyper-homology spectral sequences of Z-graded and RO(G)-graded Mackey functors for Ext and Tor over G-equivariant S-algebras (A∞ ring spectra) for finite groups G. These specialize to universal coefficient and Künneth spectral sequences.

Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ non-negative integer. $M$ $N$ two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators $\operatorname{Ext}^t_R(M, N)$ $\operatorname{H}^t_{\mathfrak a}(M)$ in terms minimal primary decomposition zero submodule which are independent choice decomposition. Then, by using...

We study the multi-dimensional persistence of Carlsson and Zomorodian [3] and obtain a finer classification based upon the higher tor-modules of a persistence module. We propose a variety structure on the set of isomorphism classes of these modules, and present several examples. We also provide a geometric interpretation for the higher tor-modules of homology modules of multi-filtered simplicia...

Abstract. A chain of c submodules E =: E0 ≥ E1 ≥ · · · ≥ Ec ≥ Ec+1 := 0 gives rise to c composable 1-cocycles in Ext1(Ei−1/Ei, Ei/Ei+1), i = 1, . . . , c. In this paper we follow the converse question: When are c composable 1-cocycles induced by a module E together with a chain of submodules as above? We call such modules c-extension modules. The case c = 1 is the classical correspondence betwe...