ON HOMOLOGICAL CLASSIFICATION OF MONOIDS BY CONDITION ＄(E^{￥prime})＄ OF RIGHT ACTS
Akbar Golchin, Hossein Mohammadzadeh Saany · The Yokohama mathematical journal = 横濱市立大學紀要. D部門, 数学 · 2007
Valdis Laan in (On a generalization of strong flatness, Acta Comment. Univ. Tartuensis 2 (1998), 55-60.) introduced Condition $(E^{\prime})$ , a generalization of Condition $(E)$ . In this paper we continue the investigation of Condition $(E^{\prime})$ and give a classification of monoids by comparing this condition of their acts with other properties. We give also a classffication of monoids for which all (monocyclic, cyclic) right acts satisfy Condition $(E^{\prime})$ and in particular for idempotent monoids and monoids $S$ with $E(S)=\{1\}$ . A classification of monoids over which all monocyclic right acts are weakly pullback flat will be given too.