2018/06/19 by M. Haddadi, Haddadi, M., seyed mojtaba naser Sheykholislami +2
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #math.RT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1806.07075
Hoenke radical, Kourosh-Amitsur radical, torsion Theory,S-act
arxiv created 2018/06/19 · openalex publication_date 2018/06/19 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In abelian categories like the category of R-modules and even in the category S-Act 0 of S-acts with a unique zero, idempotent radicals and torsion theories are equivalent, and the τ-torsion and τ- torsion free classes of a torsion theory τ are closed under coproducts. These are not necessarily true in the category S-Act of S-acts. In this paper, we prove that torsion theories are equivalent with the Kurosh- Amitsur radicals. We, also, show that the class of Kurosh-Amitsur radicals is a reflective subcategory of Hoehnke radicals, as a poset.