Morita contexts and torsions of modules

T-Radicals in the Category of Modules

“…In accordance with the definition of the T(F )-radical, we immediately obtain from [2] that W F is the largest idempotent radical λ such that λ(A) ⊂ n F (A) for all A ∈ mod-S. Therefore the inclusion W F (A) ⊂ n F (A) is always the case.…”

“…W F (A) will designate the sum of all submodules B of A ∈ mod-S such that B is a T(F )-module. W F is an idempotent radical, and T (F ) is its radical class [2]. From here on we will call this idempotent radical simply "T(F )-radical".…”

Rings and sheaves

“…The set Tor K of all torsions r on the Category of right K-modules forms a complete lattice. Here by torsion r we mean the hereditary radical on the category of modules (see [7,83,105,294,295,300,488]). …”

“…Books on the theory of rings and modules are [7,16,18,27,28,66,70,71,82,83,89,102,110,111,116,125,128,138,164,488].…”

Euclidean Combinatorial Configurations: Typology, Continuous Extensions and Representations

“…In this article the preradicals and the closure operators of module categories are studied in the case of a Morita context (R, R U S , S V R , S). of the categories R-Mod and S-Mod ( [6]). Moreover, in R-Mod we have the mappings:…”