Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101Cofree objects in the centralizer and the center categories13810066910.29252/cgasa.14.1.1ENAdnan H.AbdulwahidDepartment of Mathematics, The University of Iowa (and University of Thi-Qar), 14 MacLean Hall, 52242-1419, Iowa City, Iowa, USA.Journal Article20210131We study cocompleteness, co-wellpoweredness, and generators in the centralizer category of an object or morphism in a monoidal category, and the center or the weak center of a monoidal category. We explicitly give some answers for when colimits, cocompleteness, co-wellpoweredness, and generators in these monoidal categories can be inherited from their base monidal categories. Most importantly, we investigate cofree objects of comonoids in these monoidal categories.Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101On general closure operators and quasi factorization structures39808743510.29252/cgasa.14.1.39ENSeyed ShahinMousavi MirkalaiDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran0000-0002-2904-7692NaserHosseiniDepartment of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, IranAzadehIlaghi-HosseiniDepartment of Pure Mathematics, Faculty of Math and Computer, Shahid Bahonar University of KermanJournal Article20190108In this article the notions of quasi mono (epi) as a generalization of mono (epi), (quasi weakly hereditary) general closure operator $mathbf{C}$ on a category $mathcal{X}$ with respect to a class $mathcal{M}$ of morphisms, and quasi factorization structures in a category $mathcal{X}$ are introduced. It is shown that under certain conditions, if $(mathcal{E}, mathcal{M})$ is a quasi factorization structure in $mathcal{X}$, then $mathcal{X}$ has a quasi right $mathcal{M}$-factorization structure and a quasi left $mathcal{E}$-factorization structure. It is also shown that for a quasi weakly hereditary and quasi idempotent QCD-closure operator with respect to a certain class $mathcal{M}$, every quasi factorization structure $(mathcal{E}, mathcal{M})$ yields a quasi factorization structure relative to the given closure operator; and that for a closure operator with respect to a certain class $mathcal{M}$, if the pair of classes of quasi dense and quasi closed morphisms forms a quasi factorization structure, then the closure operator is both quasi weakly hereditary and quasi idempotent. Several illustrative examples are provided.Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101Duality theory of $p$-adic Hopf algebras811188752310.29252/cgasa.14.1.81ENTomokiMiharaUniversity of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 JapanJournal Article20200626We show the monoidal functoriality of Schikhof duality, and cultivate new duality theory of $p$-adic Hopf algebras. Through the duality, we introduce two sorts of $p$-adic Pontryagin dualities. One is a duality between discrete Abelian groups and affine formal group schemes of specific type, and the other one is a duality between profinite Abelian groups and analytic groups of specific type. We extend Amice transform to a $p$-adic Fourier transform compatible with the second $p$-adic Pontryagin duality. As applications, we give explicit presentations of a universal family of irreducible $p$-adic unitary Banach representations of the open unit disc of the general linear group and its $q$-deformation in the case of dimension $2$.Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101Schneider-Teitelbaum duality for locally profinite groups1191668752410.29252/cgasa.14.1.119ENTomokiMiharaUniversity of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 JapanJournal Article20200626We define monoidal structures on several categories of linear topological modules over the valuation ring of a local field, and study module theory with respect to the monoidal structures. We extend the notion of the Iwasawa algebra to a locally profinite group as a monoid with respect to one of the monoidal structure, which does not necessarily form a topological algebra. This is one of the main reasons why we need monoidal structures. We extend Schneider--Teitelbaum duality to duality applicable to a locally profinite group through the module theory over the generalised Iwasawa algebra, and give a criterion of the irreducibility of a unitary Banach representation.Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101Constructing the Banaschewski compactification through the functionally countable subalgebra of $C(X)$1671808751310.29252/cgasa.14.1.167ENMehdiParsiniaDepartemant of Mathematics, Shahid Chamran University of Ahvaz, Iran.Journal Article20200607Let $X$ be a zero-dimensional space and $C_c(X)$ denote the functionally countable subalgebra of $C(X)$. It is well known that $beta_0X$ (the Banaschewski compactfication of $X$) is a quotient space of $beta X$. In this article, we investigate a construction of $beta_0X$ via $beta X$ by using $C_c(X)$ which determines the quotient space of $beta X$ homeomorphic to $beta_0X$. Moreover, the construction of $upsilon_0X$ via $upsilon_{_{C_c}}X$ (the subspace ${pin beta X: forall fin C_c(X), f^*(p)<infty}$ of $beta X$) is also investigated.Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101On bornological semi-abelian algebras1812228751410.29252/cgasa.14.1.181ENFrancisBorceuxUniversit\'e de Louvain, Belgium.Maria ManuelClementinoDepartment of Mathematics, University of Coimbra, Portugal.0000-0002-2653-8090Journal Article20200607If $Bbb T$ is a semi-abelian algebraic theory, we prove that the category ${rm Born}^{Bbb T}$ of bornological $Bbb T$-algebras is homological with semi-direct products. We give a formal criterion for the representability of actions in ${rm Born}^{Bbb T}$ and, for a bornological $Bbb T$-algebra $X$, we investigate the relation between the representability of actions on $X$ as a $Bbb T$-algebra and as a bornological $Bbb T$-algebra. We investigate further the algebraic coherence and the algebraic local cartesian closedness of ${rm Born}^{Bbb T}$ and prove in particular that both properties hold in the case of bornological groups.Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101Distributive lattices and some related topologies in comparison with zero-divisor graphs2232449418810.29252/cgasa.14.1.223ENSaeidBagheriDepartment of Mathematics, Malayer University, P.O.Box: 65719-95863, Malayer, Iran.MahtabKoohi KerahroodiDepartment of Mathematics, Malayer University, P.O.Box: 65719-95863, Malayer, Iran.Journal Article20201217In this paper,<br />for a distributive lattice $mathcal L$, we study and compare some lattice theoretic features of $mathcal L$ and topological properties of the Stone spaces ${rm Spec}(mathcal L)$ and ${rm Max}(mathcal L)$ with the corresponding graph theoretical aspects of the zero-divisor graph $Gamma(mathcal L)$.<br />Among other things,<br />we show that the Goldie dimension of $mathcal L$ is equal to the cellularity of the topological space ${rm Spec}(mathcal L)$ which is also equal to the clique number of the zero-divisor graph $Gamma(mathcal L)$. Moreover, the domination number of $Gamma(mathcal L)$ will be compared with the density and the weight of the topological space ${rm Spec}(mathcal L)$.<br /><br /> For a $0$-distributive lattice $mathcal L$, we investigate the compressed subgraph $Gamma_E(mathcal L)$ of the zero-divisor graph $Gamma(mathcal L)$ and determine some properties of this subgraph in terms of some lattice theoretic objects such as associated prime ideals of $mathcal L$.<br /><br />Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585314120210101Relation between Sheffer Stroke and Hilbert algebras2452688751010.29252/cgasa.14.1.245ENTahsinOnerDepartment of Mathematics, Ege University, 35100 Izmir, Turkey0000-0002-6514-4027TugceKaticanDepartment of Mathematics, Ege University, 35100 Izmir, TurkeyArshamBorumand SaeidDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of
Kerman, Kerman, Iran.Journal Article20200607In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of Sheffer stroke and a Hilbert algebra. After it is shown that the axioms of Sheffer stroke Hilbert algebra are independent, it is given some properties of this algebraic structure. Then it is stated the relationship between Sheffer stroke Hilbert algebra and Hilbert algebra by defining a unary operation on Sheffer stroke Hilbert algebra. Also, it is presented deductive system and ideal of this algebraic structure. It is defined an ideal generated by a subset of a Sheffer stroke Hilbert algebra, and it is constructed a new ideal of this algebra by adding an element of this algebra to its ideal.