Cover for Vol. 10, No. 1. text article 2019 eng Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 0 http://cgasa.sbu.ac.ir/article_81554_55177ded07ecd0972066db23c5bdb22b.pdf An equivalence functor between local vector lattices and vector lattices Karim Boulabiar D&eacute;partement de Math&eacute;matiques Facult&eacute; des Sciences de Tunis Universit&eacute; Tunis-El Manar Campus Universitaire author text article 2018 eng We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-trivial components. Nevertheless, our main purpose is to prove, via what we call the radical functor, that the category of all vector lattices and lattice homomorphisms is equivalent to the category of local vectors lattices and unital (i.e., unit preserving) lattice homomorphisms. Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2018 1 15 http://cgasa.sbu.ac.ir/article_61405_40f76eb1944c871ec42dac7af3a5fb65.pdf State filters in state residuated lattices Zahra Dehghani Higher Education Complex of Bam, Iran author Fereshteh Forouzesh Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran. author text article 2019 eng In this paper, we introduce the notions of prime state filters, obstinate state filters, and primary state filters in state residuated lattices and study some properties of them. Several characterizations of these state filters are given and the prime state filter theorem is proved. In addition, we investigate the relations between them. Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 17 37 http://cgasa.sbu.ac.ir/article_57443_54c325a96968ad9468cd031b52f62cf4.pdf Lattice of compactifications of a topological group Wei He Institute of Mathematics, Nanjing Normal University author Zhiqiang Xiao Department of Mathematics, Nanjing Normal University, Nanjing, 210046, China. author text article 2019 eng We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological group are obtained. Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 39 50 http://cgasa.sbu.ac.ir/article_61406_5c0d76f764a8ff7460747ef9016d1a97.pdf On the property $U$-($G$-$PWP$) of acts Mostafa Arabtash Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran author Akbar Golchin Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran author Hossein Mohammadzadeh Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran author text article 2019 eng In this paper first of all we introduce Property $U$-($G$-$PWP$) of acts, which is an extension of Condition $(G$-$PWP)$ and give some general properties. Then we give a characterization of monoids when this property of acts implies some others. Also we show that the strong (faithfulness, $P$-cyclicity) and ($P$-)regularity of acts imply the property $U$-($G$-$PWP$). Finally, we give a necessary and sufficient condition under which all (cyclic, finitely generated) right acts or all (strongly, $\Re$-) torsion free (cyclic, finitely generated) right acts satisfy Property $U$-($G$-$PWP$). Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 51 67 http://cgasa.sbu.ac.ir/article_50746_67cbcf9d76aa1add1f3cea49fe75194e.pdf A Universal Investigation of $n$-representations of $n$-quivers Adnan Abdulwahid Mathematics Department, College of Computer Sciences and Mathematics, University of Thi-Qar, Iraq author text article 2019 eng \noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $\mathit{Q}_1$,$\mathit{Q}_2$,..., $\mathit{Q}_n$, we construct a new quiver $\mathscr{Q}_{\!_{(\mathit{Q}_1, \mathit{Q}_2,..., \mathit{Q}_n)}}$, called an $n$-quiver, and identify each category $Rep_k(\mathit{Q}_j)$ of representations of a quiver $\mathit{Q}_j$ as a full subcategory of the category $Rep_k(\mathscr{Q}_{\!_{(\mathit{Q}_1, \mathit{Q}_2,..., \mathit{Q}_n)}})$ of representations of $\mathscr{Q}_{\!_{(\mathit{Q}_1, \mathit{Q}_2,..., \mathit{Q}_n)}}$ for every $j \in \{1,2,\ldots , n\}$. Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 69 106 http://cgasa.sbu.ac.ir/article_63576_d0e433b72b5f2ad887b121defa6a4a09.pdf Mappings to Realcompactifications Mehdi Parsinia Departemant of Mathematics, Shahid Chamran University, Ahvaz, Iran author text article 2019 eng In this paper, we introduce and study  a mapping from the collection of all  intermediate rings of $C(X)$ to the collection of all  realcompactifications of $X$ contained in $\beta X$. By establishing the relations between this mapping and its converse,  we give a different approach to the main statements of De et. al. Using these, we provide different answers to the   four basic questions raised in Acharyya et.al. Finally, we give some notes on the realcompactifications  generated  by ideals. Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 107 116 http://cgasa.sbu.ac.ir/article_61474_334ea333a835b3a3209264236e96b85c.pdf Applications of the Kleisli and Eilenberg-Moore 2-adjunctions Juan Luis L\'opez Hernández Research Coordination, CINVCAT, P.O. Box 36620, Irapuato, Gto. M\&#039;exico. author Luis Turcio Instituto de Matem&aacute;ticas, UNAM author Adrian Vazquez-Marquez Research Coordination, Universidad Incarnate Word Campus Bajío, P.O. Box 36821, Irapuato, Gto. M\&#039;exico. author text article 2019 eng In 2010, J. Climent Vidal and J. Soliveres Tur developed, among other things, a pair of 2-adjunctions between the 2-category of adjunctions and the 2-category of monads. One is related to the Kleisli adjunction and the other to the Eilenberg-Moore adjunction for a given monad.Since any 2-adjunction induces certain natural isomorphisms of categories, these can be used to classify bijections and isomorphisms for certain structures in monad theory. In particular, one important example of a structure, lying in the 2-category of adjunctions, where this procedure can be applied to is that of a lifting. Therefore, a lifting can be characterized by the associated monad structure,lying in the 2-category of monads, through the respective 2-adjunction. The same can be said for Kleisli extensions.Several authors have been discovered this type of bijections and isomorphisms but these pair of 2-adjunctions can collect them all at once with an extra property, that of naturality. Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 117 156 http://cgasa.sbu.ac.ir/article_76725_4c74fe2ffb149c7099e49e4c27eeb355.pdf The category of generalized crossed modules Mahdieh Yavari Department of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, Iran author Alireza Salemkar Department of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, Iran author text article 2019 eng In the definition of a crossed module $(T,G,\rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${\bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate some of its categorical properties. In particular, we study the relations between epimorphisms and the surjective morphisms, and thus generalize the corresponding results of the category of (ordinary) crossed modules. By generalizing the conjugation action, we can find out what is the superiority of the conjugation to other actions. Also, we can find out a generalized crossed module with which other actions (other than the conjugation) has the properties same as a crossed module. Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 157 171 http://cgasa.sbu.ac.ir/article_69897_042894bfec4f1e44310e2fc5853f599c.pdf Persian Abstracts, Vol. 10, No. 1. text article 2019 eng Categories and General Algebraic Structures with Applications Shahid Beheshti University 2345-5853 10 v. 1 no. 2019 http://cgasa.sbu.ac.ir/article_81555_4ea74f0f68f2318b202d8deb2face8b2.pdf