On Condition (G-PWP)

Authors

  • Akbar Golchin Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
  • Hossein Mohammadzadeh Saany Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
  • Mostafa Arabtash Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
Abstract:

Laan in (Ph.D Thesis, Tartu. 1999) introduced the principal weak form of Condition $(P)$ as Condition $(PWP)$ and gave some characterization of monoids by this condition of their acts. In this paper first we introduce Condition (G-PWP), a generalization of Condition $(PWP)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. We also give a characterization of monoids, by comparing this property of their acts with some others. Finally, we give a characterization of monoids coming from some special classes, by this property of their diagonal acts and extend some results on Condition $(PWP)$ to this condition of acts.

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Journal title

volume 5  issue 1

pages  55- 84

publication date 2016-07-01

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