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ON SOME PROPERTIES OF MALCEV-NEUMANN MODULES

  • Zhao, Renyu ;
  • Liu, Zhongkui
  • Published : 2008.08.31

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* ((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* ((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* ((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

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  1. MAL'CEV–NEUMANN SERIES OVER ZIP AND WEAK ZIP RINGS vol.05, pp.04, 2012, https://doi.org/10.1142/S1793557112500581