Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 10 1 2018 05 01 An equivalence functor between local vector lattices and vector lattices 1 15 61405 EN Karim Boulabiar D&eacute;partement de Math&eacute;matiques Facult&eacute; des Sciences de Tunis Universit&eacute; Tunis-El Manar Campus Universitaire Journal Article 2017 11 13 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. http://cgasa.sbu.ac.ir/article_61405_40f76eb1944c871ec42dac7af3a5fb65.pdf
Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 10 1 2019 01 01 State filters in state residuated lattices 17 37 57443 EN Zahra Dehghani Higher Education Complex of Bam, Iran Fereshteh Forouzesh Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran. Journal Article 2017 08 01 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. http://cgasa.sbu.ac.ir/article_57443_54c325a96968ad9468cd031b52f62cf4.pdf
Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 10 1 2019 01 01 Lattice of compactifications of a topological group 39 50 61406 EN Wei He Institute of Mathematics, Nanjing Normal University Zhiqiang Xiao Department of Mathematics, Nanjing Normal University, Nanjing, 210046, China. Journal Article 2017 12 05 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. http://cgasa.sbu.ac.ir/article_61406_5c0d76f764a8ff7460747ef9016d1a97.pdf
Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 10 1 2019 01 01 On the property \$U\$-(\$G\$-\$PWP\$) of acts 51 67 50746 EN Mostafa Arabtash Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Akbar Golchin Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Hossein Mohammadzadeh Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Journal Article 2016 12 23 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\$). http://cgasa.sbu.ac.ir/article_50746_67cbcf9d76aa1add1f3cea49fe75194e.pdf
Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 10 1 2019 01 01 A Universal Investigation of \$n\$-representations of \$n\$-quivers 69 106 63576 EN Adnan Abdulwahid Mathematics Department, College of Computer Sciences and Mathematics, University of Thi-Qar, Iraq Journal Article 2017 12 22 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}\$. http://cgasa.sbu.ac.ir/article_63576_d0e433b72b5f2ad887b121defa6a4a09.pdf
Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 10 1 2019 01 01 Mappings to Realcompactifications 107 116 61474 EN Mehdi Parsinia Departemant of Mathematics, Shahid Chamran University, Ahvaz, Iran Journal Article 2017 08 28 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. <br />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. http://cgasa.sbu.ac.ir/article_61474_334ea333a835b3a3209264236e96b85c.pdf