Author/Authors :
Liang X. نويسنده Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China.
, Luo Y. نويسنده Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China.
Abstract :
There is a flatness property of acts over monoids called Condition $(PWP)$ which, so far, has received much attention. In this paper, we introduce Condition GP-$(P)$, which is a generalization of Condition $(PWP)$. Firstly, some characterizations of monoids by Condition GP-$(P)$ of their (cyclic, Rees factor) acts are given, and many known results are generalized. Moreover, some possible conditions on monoids that describe when their diagonal acts satisfy Condition GP-$(P)$ are found. Finally, using some new types of epimorphisms, an alternative description of Condition GP-$(P)$ (resp., Condition $(PWP)$) is obtained, and directed colimits of these new epimorphisms are investigated.
