We establish a link between trace modules and rigidity in modules over Noetherian rings.
We identify classes of modules which must have self-extensions and use the theory of trace …

We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian
algebras over commutative Noetherian rings. Firstly, in the introduction, we will examine its …

Let aa be an ideal in a commutative ring R. For an R-module M, we consider the small a a-
torsion Γ _ a (M)={x ∈ M ∣ ∃ n ∈ N: a^ n ⊆ (0: _Rx)\} Γ a (M)= x∈ M∣∃ n∈ N: an⊆(0: R …

The purpose of this work is to understand homological properties of structures appearing in
commutative algebra and algebraic combinatorics, objects such as commutative rings and …

The main aim of this paper is to investigate Cartan-Eilenberg complexes with respect to a
semidualizing module, and extend the existed Foxby equivalence. To this end, we define …

Let R be a commutative Noetherian ring. We give criteria for flatness of R-modules in terms
of associated primes and torsion-freeness of certain tensor products. This allows us to …

For finitely generated modules M and N over a Gorenstein local ring R, one has depth M+
depth N= depth (M⊗ RN)+ depth R, ie, the depth formula holds, if M and N are Tor …

We will only assume some basic knowledge in module theory and category theory. In
particular, we will use the following notions that can be found in any textbook on modules or …

Given an associative ring R and a torsion pair t=(T, F) in the category of left R-modules, the
heart Ht of the t-structure associated to t, is an abelian category (see [BBD]). In [HKM], the …