Monoids over which all weakly flat acts are flat
نویسندگان
چکیده
منابع مشابه
On $GPW$-Flat Acts
In this article, we present $GPW$-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right $S$-act $A_{S}$ is $GPW$-flat if for every $s in S$, there exists a natural number $n = n_ {(s, A_{S})} in mathbb{N}$ such that the functor $A_{S} otimes {}_{S}- $ preserves the embedding of the principal left ideal ${}_{S}(Ss^n)$ into ${}_{S}S$. We...
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In this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. Then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right Rees factor, cyclic and acts in general implies some other properties, respectively.
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Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regu...
متن کاملA short note on strongly flat covers of acts over monoids
Recently two different concepts of covers of acts over monoids have been studied by a number of authors and many interesting results discovered. One of these concepts is based on coessential epimorphisms and the other is based on Enochs’ definition of a flat cover of a module over a ring. Two recent papers have suggested that in the former case, strongly flat covers are not unique. We show that...
متن کامل-torsion free acts over monoids
in this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right rees factor, cyclic and acts in general implies some other properties, respectively.
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1990
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500018198