منابع مشابه
SEQUENTIALLY COMPACT S-ACTS
The investigation of equational compactness was initiated by Banaschewski and Nelson. They proved that pure injectivity is equivalent to equational compactness. Here we define the so called sequentially compact acts over semigroups and study some of their categorical and homological properties. Some Baer conditions for injectivity of S-acts are also presented.
متن کاملOn $GPW$-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...
متن کاملOn Regularity of Acts
In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...
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.
متن کاملIntersection graphs associated with semigroup acts
The intersection graph $mathbb{Int}(A)$ of an $S$-act $A$ over a semigroup $S$ is an undirected simple graph whose vertices are non-trivial subacts of $A$, and two distinct vertices are adjacent if and only if they have a non-empty intersection. In this paper, we study some graph-theoretic properties of $mathbb{Int}(A)$ in connection to some algebraic properties of $A$. It is proved that the fi...
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ژورنال
عنوان ژورنال: CFA Institute Magazine
سال: 2015
ISSN: 1543-1398
DOI: 10.2469/cfm.v26.n2.9