ON HOMOLOGICAL CLASSIFICATION OF MONOIDS BY CONDITION ＄(E^{￥prime})＄ OF RIGHT ACTS
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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 classification 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 at will be given too.
- Yokohama City University and Yokohama National Universityの論文
- 2007-00-00
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