Arabtash, M., Golchin, A., Mohammadzadeh Saany, H. (2016). On Condition (G-PWP). Categories and General Algebraic Structures with Applications, 5(1), 55-84.

Mostafa Arabtash; Akbar Golchin; Hossein Mohammadzadeh Saany. "On Condition (G-PWP)". Categories and General Algebraic Structures with Applications, 5, 1, 2016, 55-84.

Arabtash, M., Golchin, A., Mohammadzadeh Saany, H. (2016). 'On Condition (G-PWP)', Categories and General Algebraic Structures with Applications, 5(1), pp. 55-84.

Arabtash, M., Golchin, A., Mohammadzadeh Saany, H. On Condition (G-PWP). Categories and General Algebraic Structures with Applications, 2016; 5(1): 55-84.

^{}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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