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

Document Type : Research Paper

Authors

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

10.29252/cgasa.10.1.51

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

Keywords

References

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Categories and General Algebraic Structures with Applications
Volume 10, Issue 1
January 2019
Pages 51-67

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