Arabtash, M., Golchin, A., Mohammadzadeh, H. (2019). On the property $U$-($G$-$PWP$) of acts. Categories and General Algebraic Structures with Applications, 10(1), 51-67.

Mostafa Arabtash; Akbar Golchin; Hossein Mohammadzadeh. "On the property $U$-($G$-$PWP$) of acts". Categories and General Algebraic Structures with Applications, 10, 1, 2019, 51-67.

Arabtash, M., Golchin, A., Mohammadzadeh, H. (2019). 'On the property $U$-($G$-$PWP$) of acts', Categories and General Algebraic Structures with Applications, 10(1), pp. 51-67.

Arabtash, M., Golchin, A., Mohammadzadeh, H. On the property $U$-($G$-$PWP$) of acts. Categories and General Algebraic Structures with Applications, 2019; 10(1): 51-67.

^{}Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

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 $U$-($G$-$PWP$).

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