The notion of naive lifting of DG modules was introduced by the authors in [16, 17] for the
purpose of studying problems in homological commutative algebra that involve self …

This paper is a sequel to [L. Positselski, Dedualizing complexes and MGM duality, J. Pure
Appl. Algebra 220 (12)(2016) 3866–3909, arXiv: 1503.05523 [math. CT]; Contraadjusted …

We study modules over a commutative artin local ring R. For the most part, we concentrate
on almost split sequences with uniserial modules in its end terms. Based on our …

Let A be a commutative noetherian ring, let a⊆ A be an ideal, and let J be an injective A-
module. A basic result in the structure theory of injective modules states that the A-module …

The long-standing Auslander and Reiten Conjecture states that a finitely generated module
over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several authors …

Let R and S be rings and SCR a semidualizing bimodule. We investigate the relative Tor
functors Tor i ℳ ℒ C (−,−) Tor_i^ML_C(-,-) defined via C-level resolutions, and these functors …

We introduce the notion of torsion-simple objects in an abelian category: these are the
objects which are always either torsion or torsion-free with respect to any torsion pair. We …

Given finitely generated modules M and N over a local ring R, the tensor product M⊗ RN
typically has nonzero torsion. Indeed, the assumption that the tensor product is torsion-free …

This thesis is a study of generalizations of the dual concepts of an artinian module and a
noetherian module, called a semiartinian module and a seminoetherian module …

We determine the submodule of finite support of the tensor product of two modules $ M $
and $ N $ over a local ring and estimate its length in terms of $ M $ and $ N $. Also, we …