On a generalization of condition (PWP)
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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.
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Journal title
volume 42 issue 5
pages 1057- 1076
publication date 2016-11-01
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