$\scr{Z^{ \ast}}$ - semilocal modules and the proper class $\scr{RS}$

• Datum: 2019
• Hauptverfasser: Türkmen, E., Тюркмен, Є.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2019
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1447
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

Over an arbitrary ring, a module $M$ is said to be $\scr{Z^{ \ast}}$ -semilocal if every submodule $U$ of $M$ has a $\scr{Z^{ \ast}}$ -supplement $V$ in $M$, i.e., $M = U + V$ and $U \cap V \subseteq \scr{Z^{ \ast}} (V )$, where $\scr{Z^{ \ast}}(V ) = \{m \in V | Rm$ is a small module $\}$ is...