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We consider monoids $S=G\dot \cup I$ where G is a group and I is an ideal of S and show that if an S-act is principally weakly flat, (weakly) flat, torsion free or satisfies conditions (P) or (PE) as an I1-act, then it has these properties as an S-act. We also show that an S-act which is free, projective or strongly flat as an I1-act may not generally have these properties as an S-act.  相似文献
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In this paper by a new proof we will show that most of flatness properties of acts over monoids can be transferred to their coproduct and vice versa.  相似文献
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We consider monoids $S=G\;\dot{\cup}\; I$ where $G$ is a group and $I$ is an ideal of $S$ and show that if an $S$-act is principally weakly homoflat or weakly homoflat as an $I^1$-act, then it has these properties as an $S$-act. We also show that an $S$-act which is (weakly) pullback flat, equalizer flat, (principally) weakly kernel flat, translation kernel flat or satisfies Condition $(E)$ as an $I^1$-act may not generally have these properties as an $S$-act. The flatness notions considered in this paper were introduced in {\it V. Laan, Pullbacks and flatness properties of acts I, Comm. Alg. ${\bf 29}(2)$ (2001), 829--850}.  相似文献
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Laan in (Acta Comment. Univ. Tartu Math., 2:55–60, 1998) introduced Condition (E′). In Golchin and Mohammadzadeh (Yokohama Math. J., 54:79–88, 2007) we gave a characterization of monoids by this condition of their acts. In this paper similar to Condition (E′), we introduce a generalization of Condition (P) called Condition (P′) and will give a characterization of monoids by this condition of their (Rees factor) acts.  相似文献
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By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong (P)-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.  相似文献
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We consider pomonoids , where G is a pogroup and I is a poideal of S and show that if an S-poset is principally weakly flat, (weakly) flat, po-flat, (principally) weakly po-flat, (po-) torsion free or satisfies Conditions (P), (P E ), (P w ), (PWP), (PWP) w , (WP) or (WP) w as an I 1-poset, then it has these properties as an S-poset. We also show that an S-poset which is free, projective or strongly flat as an I 1-poset may not generally have these properties as an S-poset.  相似文献
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In [5 Laan , V. ( 2001 ). Pullbacks and flatness proprties of acts I . Comm. Algebra. 29 ( 2 ): 829850 .[Taylor & Francis Online], [Web of Science ®] [Google Scholar], pp. 829–850] study was initiated of flatness properties of right acts A S over a monoid S that can be described in terms when the functor A S ⊗-preserves pullbacks. In that article, familiar flatness properties emerged in a new light, and new properties such as (PWP) and (WP) were discovered. In this article, we extend these results to S-posets. Also we introduce Conditions (WP) w and (PWP) w and consider the relation between them and Conditions (WP), (PWP), and po-flatness.  相似文献
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