On complementability of certain generalized hypercenters in Artinian modules

• Date: 1997
• Main Authors: Kurdachenko, L. A., Petrenko, B. V., Subbotin, I. Ya., Курдаченко, Л. А., Петренко, Б. В., Суботін, І. Я.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1997
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5154
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.