2021-07-26T06:19:51Z
https://cgasa.sbu.ac.ir/?_action=export&rf=summon&issue=14820
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Cover for Vol. 14, No. 1.
2021
01
01
https://cgasa.sbu.ac.ir/article_100670_e7db302c21a29404625dae55bc4b5ad0.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Cofree objects in the centralizer and the center categories
Adnan H.
Abdulwahid
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
2021
01
01
1
38
https://cgasa.sbu.ac.ir/article_100669_4c34698930621a134561e3dada358da3.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
On general closure operators and quasi factorization structures
Seyed Shahin
Mousavi Mirkalai
Naser
Hosseini
Azadeh
Ilaghi-Hosseini
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
2021
01
01
39
80
https://cgasa.sbu.ac.ir/article_87435_57be9bc0e817ada7c5f3c927f59226c3.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Duality theory of $p$-adic Hopf algebras
Tomoki
Mihara
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
2021
01
01
81
118
https://cgasa.sbu.ac.ir/article_87523_90bb198d291c498c8cd128ce4c24faad.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Schneider-Teitelbaum duality for locally profinite groups
Tomoki
Mihara
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
2021
01
01
119
166
https://cgasa.sbu.ac.ir/article_87524_0a893e28ec798a2b4354b71165849781.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Constructing the Banaschewski compactification through the functionally countable subalgebra of $C(X)$
Mehdi
Parsinia
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 $\{p\in \beta X: \forall f\in C_c(X), f^*(p)<\infty\}$ of $\beta X$) is also investigated.
Zero-dimensional space
functionally countable subalgebra
Stone-$rm{check{C}}$ech compactification
Banaschewski compactification
2021
01
01
167
180
https://cgasa.sbu.ac.ir/article_87513_b8f15e9052fb623c491eaaabd5b1e01e.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
On bornological semi-abelian algebras
Francis
Borceux
Maria Manuel
Clementino
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
2021
01
01
181
222
https://cgasa.sbu.ac.ir/article_87514_6bd7fb9a1c7583f5b8f3b7873d4350bb.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Distributive lattices and some related topologies in comparison with zero-divisor graphs
Saeid
Bagheri
mahtab
Koohi Kerahroodi
In this paper,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 $\Gamma(\mathcal L)$.Among other things,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 ${\rm Spec}(\mathcal L)$. 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 $\mathcal L$.
Distributive lattice
Goldie dimension
compressed zero-divisor graph
domination number
2021
01
01
223
244
https://cgasa.sbu.ac.ir/article_94188_8886cc33fcfa95bf3e8a98c714546517.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Relation between Sheffer Stroke and Hilbert algebras
Tahsin
Oner
Tugce
Katican
Arsham
Borumand Saeid
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
2021
01
01
245
268
https://cgasa.sbu.ac.ir/article_87510_0c7d162f32c37f1f0916408dfd6b27ae.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2021
14
1
Persian Abstracts, Vol. 14, No. 1.
2021
01
01
https://cgasa.sbu.ac.ir/article_100671_dddeddbd707d3abd9b872a48f7583fd4.pdf