TY - JOUR ID - 50746 TI - On the property $U$-($G$-$PWP$) of acts JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Arabtash, Mostafa AU - Golchin, Akbar AU - Mohammadzadeh, Hossein AD - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Y1 - 2019 PY - 2019 VL - 10 IS - 1 SP - 51 EP - 67 KW - $S$-act KW - condition ($PWP$) KW - condition ($G$-$PWP$) KW - $U$-($G$-$PWP$) DO - 10.29252/cgasa.10.1.51 N2 - 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 $U$-($G$-$PWP$). UR - https://cgasa.sbu.ac.ir/article_50746.html L1 - https://cgasa.sbu.ac.ir/article_50746_67cbcf9d76aa1add1f3cea49fe75194e.pdf ER -