5 papers
On the natural transformations of extension functors
Abdolnaser Bahlekeh, Shokrollah Salarian
Assume that $\C$ is an exact category. This paper is concerned with the natural transformations between extension functors on $\C$. The first main result indicates that if $\C$ has…
On the vanishing of Ext and Tor
Abdolnaser Bahlekeh, Shokrollah Salarian
This paper contains two theorems concerning the vanishing of natural transformations of (co)homology functors. Precisely, assume that is a right noetherian ring and $f: M\rt N$…
phantom stable categories of -Frobenius categories are triangulated
Abdolnaser Bahlekeh, Fahimeh Sadat Fotouhi, Shokrollah Salarian +1
Let be a non-negative integer. Motivated by the universal property of the stable category of Frobenius categories, the authors in \cite{bfss} generalized the stabilization of F…
Representation-theoretic properties of balanced big Cohen-Macaulay modules
Abdolnaser Bahlekeh, Fahimeh Sadat Fotouhi, Shokrollah Salarian
Let $(R, \m, k)$ be a complete Cohen-Macaulay local ring. In this paper, we assign a numerical invariant, for any balanced big Cohen-Macaulay module, called $\uh$-length. Among oth…
Phantom stable category of -Frobenius categories
Abdolnaser Bahlekeh, Fahimeh Sadat Fotouhi, Shokrollah Salarian +1
Let be a non-negative integer. An exact category $\C$ is said to be an -Frobenius category, provided that it has enough -projectives and -injectives and the -projec…