Characterization of monoids by ($U$-)$GPW$-flatness of right acts

Abstract

The authors in 2020 introduced $GPW$-flatness and gave a characterization of monoids by this property of their right acts. In this article we continue this investigation and will give a characterization of monoids by this condition of their right Rees factor acts. Also we give a characterization of monoids by comparing this property of their right acts with other properties.We also introduce $U$-$GPW$-flatness of acts, which is an extension of $GPW$-flatness and give some general properties and a characterization of monoids when this property of acts implies some others and vice versa.

Keywords

• gpw-flat
• gpw-left stabilizing
• u-gpw-flat