Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
Cofree objects in the centralizer and the center categories
1
38
EN
Adnan H.
Abdulwahid
Department of Mathematics, The University of Iowa (and University of Thi-Qar), 14 MacLean Hall, 52242-1419, Iowa City, Iowa, USA.
adnan-al-khafaji@uiowa.edu
10.29252/cgasa.14.1.1
We 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.
category,center,comonoid,cocompleteness,co-wellpoweredness
https://cgasa.sbu.ac.ir/article_100669.html
https://cgasa.sbu.ac.ir/article_100669_4c34698930621a134561e3dada358da3.pdf
Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
On general closure operators and quasi factorization structures
39
80
EN
Seyed Shahin
Mousavi Mirkalai
0000-0002-2904-7692
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
smousavi@uk.ac.ir
Naser
Hosseini
Department of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, Iran
nhoseini@uk.ac.ir
Azadeh
Ilaghi-Hosseini
Department of Pure Mathematics, Faculty of Math and Computer, Shahid Bahonar University of Kerman
a.ilaghi@math.uk.ac.ir
10.29252/cgasa.14.1.39
In 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.
Quasi mono (epi),quasi (right,left) factorization structure,(quasi weakly hereditary,quasi idempotent) general closure operator
https://cgasa.sbu.ac.ir/article_87435.html
https://cgasa.sbu.ac.ir/article_87435_57be9bc0e817ada7c5f3c927f59226c3.pdf
Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
Duality theory of $p$-adic Hopf algebras
81
118
EN
Tomoki
Mihara
University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 Japan
mihara@math.tsukuba.ac.jp
10.29252/cgasa.14.1.81
We 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 $2$.
Pontryagin duality,$p$-adic,Hopf
https://cgasa.sbu.ac.ir/article_87523.html
https://cgasa.sbu.ac.ir/article_87523_90bb198d291c498c8cd128ce4c24faad.pdf
Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
Schneider-Teitelbaum duality for locally profinite groups
119
166
EN
Tomoki
Mihara
University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 Japan
mihara@math.tsukuba.ac.jp
10.29252/cgasa.14.1.119
We 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.
Iwasawa theory,p-adic,locally profinite group
https://cgasa.sbu.ac.ir/article_87524.html
https://cgasa.sbu.ac.ir/article_87524_0a893e28ec798a2b4354b71165849781.pdf
Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
Constructing the Banaschewski compactification through the functionally countable subalgebra of $C(X)$
167
180
EN
Mehdi
Parsinia
Departemant of Mathematics, Shahid Chamran University of Ahvaz, Iran.
parsiniamehdi@gmail.com
10.29252/cgasa.14.1.167
Let $X$ 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.
Zero-dimensional space,functionally countable subalgebra,Stone-$rm{check{C}}$ech compactification,Banaschewski compactification
https://cgasa.sbu.ac.ir/article_87513.html
https://cgasa.sbu.ac.ir/article_87513_b8f15e9052fb623c491eaaabd5b1e01e.pdf
Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
On bornological semi-abelian algebras
181
222
EN
Francis
Borceux
Universit\'e de Louvain, Belgium.
francis.borceux@uclouvain.be
Maria Manuel
Clementino
0000-0002-2653-8090
Department of Mathematics, University of Coimbra, Portugal.
mmc@mat.uc.pt
10.29252/cgasa.14.1.181
If $Bbb T$ 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.
Semi-abelian algebraic theory,bornology,bornological algebra,bornological group,action representability,algebraic coherence,local algebraic cartesian closedness
https://cgasa.sbu.ac.ir/article_87514.html
https://cgasa.sbu.ac.ir/article_87514_6bd7fb9a1c7583f5b8f3b7873d4350bb.pdf
Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
Distributive lattices and some related topologies in comparison with zero-divisor graphs
223
244
EN
Saeid
Bagheri
Department of Mathematics, Malayer University, P.O.Box: 65719-95863, Malayer, Iran.
s.bagheri@malayeru.ac.ir
mahtab
Koohi Kerahroodi
Department of Mathematics, Malayer University, P.O.Box: 65719-95863, Malayer, Iran.
mhbkoohi@gmail.com
10.29252/cgasa.14.1.223
In 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 />
Distributive lattice,Goldie dimension,compressed zero-divisor graph,domination number
https://cgasa.sbu.ac.ir/article_94188.html
https://cgasa.sbu.ac.ir/article_94188_8886cc33fcfa95bf3e8a98c714546517.pdf
Shahid Beheshti University
Categories and General Algebraic Structures with Applications
2345-5853
2345-5861
14
1
2021
01
01
Relation between Sheffer Stroke and Hilbert algebras
245
268
EN
Tahsin
Oner
0000-0002-6514-4027
Department of Mathematics, Ege University, 35100 Izmir, Turkey
tahsin.oner@ege.edu.tr
Tugce
Katican
Department of Mathematics, Ege University, 35100 Izmir, Turkey
tugcektcn@gmail.com
Arsham
Borumand Saeid
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of
Kerman, Kerman, Iran.
arsham@uk.ac.ir
10.29252/cgasa.14.1.245
In 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.
Hilbert algebra,Sheffer stroke,Sheffer stroke Hilbert algebra
https://cgasa.sbu.ac.ir/article_87510.html
https://cgasa.sbu.ac.ir/article_87510_0c7d162f32c37f1f0916408dfd6b27ae.pdf