Popa, Valeriu On mixed LCA groups with commutative rings of continuous endomorphisms. (English) Zbl 1143.22003 Bul. Acad. Ştiinţe Repub. Mold., Mat. 2007, No. 3(55), 73-90 (2007). This paper is a continuation of papers by the author [Bul. Acad. Ştiinţe Repub. Mold., Mat. 2006, No. 3(52), 87–100 (2006; Zbl 1180.22007); ibid., 2007, No. 1(53), 83–94 (2007; Zbl 1129.22003); ibid., Mat. 2007, No. 2(54), 81–100 (2007)] in which certain results concerning the commutativity of the endomorphism rings of Abelian groups are extended to LCA groups.In the paper under review sufficient conditions are given under which the ring \(End_c(A)\) of continuous endomorphisms of a mixed LCA group \(A\) is commutative. The case of discrete Abelian groups was treated in [T. Szele and J. Szendrei, Acta Math. Acad. Sci. Hung. 2, 309–324 (1951; Zbl 0044.25404)]. Reviewer’s remark. There is a confusion of the terms used by the author. The author refers to [N. Bourbaki, Obščaja topologija. Topologičeskie gruppy. Čisla i svjazannye s nimi gruppy i prostranstva. Moskva, 1969; Zbl 0197.30402. Translation of the French original] for the term local direct product but the corresponding notion is called in Bourbaki’s text local product. Reviewer: Mihail I. Ursul (Oradea) MSC: 22B05 General properties and structure of LCA groups 16W80 Topological and ordered rings and modules Keywords:LCA group; ring of continuous endomorphisms; mixed group; pure subgroup Citations:Zbl 1129.22003; Zbl 0044.25404; Zbl 1180.22007; Zbl 0197.30402 PDFBibTeX XMLCite \textit{V. Popa}, Bul. Acad. Științe Repub. Mold., Mat. 2007, No. 3(55), 73--90 (2007; Zbl 1143.22003)