Characterization of Monoids by Condition (PWP_{S}) of right acts

In [۸] Valdis Laan introduced Condition (PW P). Golchin and Mohammadzadeh in [۳] introduced Condition (PW P_E), such that Condition (PW P) implies it but the converse is not true in general. In this paper at first we introduce a generalization of Condition (PW P_E), called Condition (PW P_S). Then will give some general properties and a characterization of monoids for which all right acts satisfy this condition. Also, we give a characterization of monoids, by comparing this property of their acts with some others. Finally, we will give a characterization of monoid S, for which S^{I}_{S}, for any non-empty set I and S^{S \times S}_{S}, satisfy Condition(PW P_S).

کلیدواژه ها:

Right S-act ، Condition (PWP_S) ، Left PP monoid