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:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۵، صفحات ۱۰۵۷-۱۰۷۶
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