2021-01-22T18:26:07Z
http://cgasa.sbu.ac.ir/?_action=export&rf=summon&issue=11663
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
Cover for Vol. 12, No. 1.
2020
01
01
http://cgasa.sbu.ac.ir/article_87446_a7e000c9d66011a5abdb6400f8446452.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
Witt rings of quadratically presentable fields
Pawel
Gladki
Krzysztof
Worytkiewicz
This paper introduces an approach to the axiomatic theory of quadratic forms based on $presentable$ partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of $quadratically\ presentable\ fields$, that is, fields equipped with a presentable partial order inequationaly compatible with the algebraic operations. In particular, Witt rings of symmetric bilinear forms over fields of arbitrary characteristics are isomorphic to Witt rings of suitably built quadratically presentable fields.
Quadratically presentable fields
Witt rings
hyperfields
quadratic forms
2020
01
01
1
23
http://cgasa.sbu.ac.ir/article_87412_e4ca569b071e83128b5db22ac6d06101.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
On $GPW$-Flat Acts
Hamideh
Rashidi
Akbar
Golchin
Hossein
Mohammadzadeh Saany
In this article, we present $GPW$-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right $S$-act $A_{S}$ is $GPW$-flat if for every $s \in S$, there exists a natural number $n = n_ {(s, A_{S})} \in \mathbb{N}$ such that the functor $A_{S} \otimes {}_{S}- $ preserves the embedding of the principal left ideal ${}_{S}(Ss^n)$ into ${}_{S}S$. We show that a right $S$-act $A_{S}$ is $GPW$-flat if and only if for every $s \in S$ there exists a natural number $n = n_{(s, A_{S})} \in \mathbb{N}$ such that the corresponding $\varphi$ is surjective for the pullback diagram $P(Ss^n, Ss^n, \iota, \iota, S)$, where $\iota : {}_{S}(Ss^n) \rightarrow {}_{S}S$ is a monomorphism of left $S$-acts. Also we give some general properties and a characterization of monoids for which this condition of their acts implies some other properties and vice versa.
$GPW$-flat
Eventually regular monoid
Eventually left almost regular monoid
2020
01
01
25
42
http://cgasa.sbu.ac.ir/article_82637_db225e4212ba0171013678302be2c9d2.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
$(m,n)$-Hyperideals in Ordered Semihypergroups
Ahsan
Mahboob
Noor
Khan
Bijan
Davvaz
In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideals, respectively. The relations ${_m\mathcal{I}}, \mathcal{I}_n, \mathcal{H}_m^n$, and $\mathcal{B}_m^n$ on an ordered semihypergroup are, then, introduced. We prove that $\mathcal{B}_m^n \subseteq \mathcal{H}_m^n$ on an ordered semihypergroup and provide a condition under which equality holds in the above inclusion. We also show that the $(m,0)$-regularity [$(0,n)$-regularity] of an element induce the $(m,0)$-regularity [$(0,n)$-regularity] of the whole $\mathcal{H}_m^n$-class containing that element as well as the fact that $(m,n)$-regularity and $(m,n)$-right weakly regularity of an element induce the $(m,n)$-regularity and $(m,n)$-right weakly regularity of the whole $\mathcal{B}_m^n$-class and $\mathcal{H}_m^n$-class containing that element, respectively.
Ordered semihypergroups
$(m,0)$-hyperideals
$(0,n)$-hyperideals
2020
01
01
43
67
http://cgasa.sbu.ac.ir/article_87415_1fd525cccd124d58a33309087242f95f.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
On exact category of $(m, n)$-ary hypermodules
Najmeh
Jafarzadeh
Reza
Ameri
We introduce and study category of $(m, n)$-ary hypermodules as a generalization of the category of $(m, n)$-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on $(m, n)$-hypermodules, as an important tool in the study of algebraic hyperstructures and prove that this relation is really functorial, that is, we introduce the fundamental functor from the category of $(m, n)$-hypermodules to the category $(m, n)$-modules and prove that it preserves monomorphisms. Finally, we prove that the category of $(m, n)$-hypermodules is an exact category, and, hence, it generalizes the classical case.
$(m,n)$-hypermodules
kernel
cokernel
balanced category
fundamental functor
exact category
2020
01
01
69
88
http://cgasa.sbu.ac.ir/article_80792_907e526521584c03372aaada0e600e45.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
From torsion theories to closure operators and factorization systems
Marco
Grandis
George
Janelidze
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
Exact sequence
torsion theory
closure operator
factorization system
ideal of null morphisms
2020
01
01
89
121
http://cgasa.sbu.ac.ir/article_87116_929764e335e7d4c92a5611139b9e065a.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
Some aspects of cosheaves on diffeological spaces
Alireza
Ahmadi
Akbar
Dehghan Nezhad
We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar\'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of the D-topological structure. We also study quasi-cosheaves, defined by pre-cosheaves which respect the colimit over covering generating families, and prove that cosheaves are quasi-cosheaves. Finally, a so-called quasi-\v{C}ech homology with values in pre-cosheaves is established for diffeological spaces.
Cosheaves
quasi-cosheaves
site of plots
covering generating families
quasi-v{C}ech homology
diffeological spaces
2020
01
01
123
147
http://cgasa.sbu.ac.ir/article_87119_6b625005860bfe6a4bd5da17a099b89b.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
The notions of closedness and D-connectedness in quantale-valued approach spaces
Muhammad
Qasim
Samed
Ozkan
In this paper, we characterize local $T_{0}$ and $T_{1}$ quantale-valued gauge spaces, show how these concepts are related to each other and apply them to $\mathcal{L}$-approach distance spaces and $\mathcal{L}$-approach system spaces. Furthermore, we give the characterization of a closed point and $D$-connectedness in quantale-valued gauge spaces. Finally, we compare all these concepts to each other.
$mathcal{L}$-approach distance space
$mathcal{L}$-gauge space
topological category
Separation
closedness
D-connectedness
2020
01
01
149
173
http://cgasa.sbu.ac.ir/article_87411_0927cf623a93d8d592cac3c1677607b0.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
Classification of monoids by Condition $(PWP_{ssc})$
Pouyan
Khamechi
Hossein
Mohammadzadeh Saany
Leila
Nouri
Condition $(PWP)$ which was introduced in (Laan, V., {\it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({\it On Condition $(PWP_E)$}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition $(PWP_E)$, such that Condition $(PWP)$ implies it, that is, Condition $(PWP_E)$ is a generalization of Condition $(PWP)$. In this paper we introduce Condition $(PWP_{ssc})$, which is much easier to check than Conditions $(PWP)$ and $(PWP_E)$ and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition $(PWP_{ssc})$ will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition $(PWP_{ssc})$ and also a classification of monoids $S$ will be given for which all right $S$-acts satisfying some other flatness properties have Condition $(PWP_{ssc})$.
$S$-act
Flatness properties
Condition $(PWP_{ssc})$
semi-cancellative
$e$-cancellative
2020
01
01
175
197
http://cgasa.sbu.ac.ir/article_85729_9d3888f3fd18b864c1967d267a21ae2c.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2020
12
1
Persian Abstracts, Vol. 11, No. 1.
2020
01
01
http://cgasa.sbu.ac.ir/article_87447_30e3ae686ac4b95893d47c5aff5815fc.pdf