فهرست مطالب مصطفی عربتاش

In this paper first of all we introduce Property U-(G-PWP) of acts, which is an extension of Condition (G-PWP) and give some general properties. Then we give a characterization of monoids when this property of acts implies some others. Also we show that the strong (faithfulness, P-cyclicity) and (P-)regularity of acts imply the property U-(G-PWP). Finally, we give a necessary and sufficient condition under which all (cyclic, finitely generated) right acts or all (strongly, R-) torsion free (cyclic, finitely generated) right acts satisfy Property U-(G-PWP).

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.