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.1806.07077
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
Various generalizations of the concept of injectivy, in particular injectivy with respect to a specific class of morphisms, have been intensively studied throughout the years in different categories. One of the important kinds of injectivy studied in the category R-Mod of R-modules is τ-injectivy, for a torsion theory τ, or in the other words r-injectivy, where r is the induced idempotent radical by τ. In this paper, we introduce the notion of r-injectivy, for a Hoehnke radical r in the category S-Act of S-acts and we study the main properties of this kind of injectivy. Indeed, we show that this kind of injectivy is well behavior and also we present a Bear Theorem for r-injective S-acts. We then consider r-injectivy for a Kurosh-Amitsur radical r and we give stronger results in this case. Finally we present conditions under which r-injective S-acts are exactly injective ones and we give a characterization for injective S-acts