@article { author = {Arabtash, Mostafa and Golchin, Akbar and Mohammadzadeh Saany, Hossein}, title = {On Condition (G-PWP)}, journal = {Categories and General Algebraic Structures with Applications}, volume = {5}, number = {1}, pages = {55-84}, year = {2016}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {}, 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 = {$S$-act,condition ($PWP$),condition ($G$-$PWP$)}, url = {https://cgasa.sbu.ac.ir/article_13905.html}, eprint = {https://cgasa.sbu.ac.ir/article_13905_e158b94d9effd3026710c9030d20f056.pdf} }