# On Condition (G-PWP)

Document Type : Research Paper

Authors

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.

Keywords

#### References

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