Bunu, I. D.; Goyan, I. M.; Tèbyrtsè, E. I. On essentially left-Artinian rings. (Russian) Zbl 0714.16014 Mat. Issled. 111, 51-54 (1989). The ring R is named essentially left Artinian if it contains some essential Artinian left ideal. A pretorsion r of the category \({}_ R{\mathfrak M}\) is named: 1) ideal, if its filter F(r) is closed relative to arbitrary intersections; 2) coessential, if from \(r\cap t=\epsilon\) follows \(t=\epsilon\), where \(\epsilon (M)=M\) for every \(M\in_ R{\mathfrak M}\). A ring R is essentially left Artinian iff Goldie’s pretorsion z in \({}_ R{\mathfrak M}\) is ideal and coessential and every pretorsion \(r>z\) in \({}_ R{\mathfrak M}\) is ideal. As a corollary is obtained the following description of semisimple Artinian rings: semiprime rings R for which all pretorsions in \({}_ R{\mathfrak M}\) are ideal. Reviewer: A.I.Kashu MSC: 16P20 Artinian rings and modules (associative rings and algebras) 16S90 Torsion theories; radicals on module categories (associative algebraic aspects) 16N60 Prime and semiprime associative rings Keywords:essentially left Artinian; essential Artinian left ideal; Goldie’s pretorsion; semisimple Artinian rings; semiprime rings PDFBibTeX XMLCite \textit{I. D. Bunu} et al., Mat. Issled. 111, 51--54 (1989; Zbl 0714.16014) Full Text: EuDML