On the property U-(G-PWP) of acts

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, \Re-) torsion free (cyclic, finitely generated) right acts satisfy Property U-(G-PWP).

Keywords:

S-act , condition (PWP) , condition (G-PWP) , U-(G-PWP)