On some properties of Malcev-Neumann modules
Bull. Korean Math. Soc. 2008 Vol. 45, No. 3, 445-456
Published online September 1, 2008
Renyu Zhao and Zhongkui Liu
Northwest Normal University, Northwest Normal University
Abstract : Let $M$ be a right $R$-module, $G$ an ordered group and $\sigma$ a map from $G$ into the group of automorphisms of $R$. The conditions under which the Malcev-Neumann module $M\ast((G))$ is a PS module and a p.q.Baer module are investigated in this paper. It is shown that: (1) If $M_{R}$ is a reduced $\sigma$-compatible module, then the Malcev-Neumann module $M\ast((G))$ over a PS-module is also a PS-module; (2) If $M_{R}$ is a faithful $\sigma$-compatible module, then the Malcev-Neumann module $M\ast((G))$ is a p.q.Baer module if and only if the right annihilator of any $G$-indexed family of cyclic submodules of $M$ in $R$ is generated by an idempotent of $R$.
Keywords : Malcev-Neumann module, Malcev-Neumann ring, PS-module, p.q.Baer module
MSC numbers : 16W60
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