• 제목/요약/키워드: Malcev-Neumann ring

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ON SOME PROPERTIES OF MALCEV-NEUMANN MODULES

  • Zhao, Renyu;Liu, Zhongkui
    • 대한수학회보
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    • 제45권3호
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    • pp.445-456
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    • 2008
  • 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.