Cover for Vol. 12, No. 1.
text
article
2020
eng
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
http://cgasa.sbu.ac.ir/article_87446_a7e000c9d66011a5abdb6400f8446452.pdf
Witt rings of quadratically presentable fields
Pawel
Gladki
Institute of Mathematics, Faculty of Mathematics, Physics and Chemistry, University of Silesia
author
Krzysztof
Worytkiewicz
Laboratorire de Math'{e}matiques, Universit'{e} Savoie Mont Blanc, B^{a}timent Le Chablais, Campus Scientifique, 73376 Le Bourget du Lac, France.
author
text
article
2020
eng
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.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
1
23
http://cgasa.sbu.ac.ir/article_87412_e4ca569b071e83128b5db22ac6d06101.pdf
dx.doi.org/10.29252/cgasa.12.1.1
On $GPW$-Flat Acts
Hamideh
Rashidi
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
author
Akbar
Golchin
University of Sistan and Baluchestan
author
Hossein
Mohammadzadeh Saany
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
author
text
article
2020
eng
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.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
25
42
http://cgasa.sbu.ac.ir/article_82637_db225e4212ba0171013678302be2c9d2.pdf
dx.doi.org/10.29252/cgasa.12.1.25
$(m,n)$-Hyperideals in Ordered Semihypergroups
Ahsan
Mahboob
Aligarh Muslim University
author
Noor
Khan
Aligarh Muslim University
author
Bijan
Davvaz
Yazd University
author
text
article
2020
eng
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.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
43
67
http://cgasa.sbu.ac.ir/article_87415_1fd525cccd124d58a33309087242f95f.pdf
dx.doi.org/10.29252/cgasa.12.1.43
On exact category of $(m, n)$-ary hypermodules
Najmeh
Jafarzadeh
Department of Mathematics, Payamenoor University,P.O. Box 19395-3697, Tehran, Iran.
author
Reza
Ameri
Mathematics, School of Mathematics, Statistics and Computer
Science, University of Tehran
author
text
article
2020
eng
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.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
69
88
http://cgasa.sbu.ac.ir/article_80792_907e526521584c03372aaada0e600e45.pdf
dx.doi.org/10.29252/cgasa.12.1.69
From torsion theories to closure operators and factorization systems
Marco
Grandis
Dipartimento di Matematica, Universit\`a di Genova, Via Dodecaneso 35,
16146-Genova, Italy
author
George
Janelidze
Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa.
author
text
article
2020
eng
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].
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
89
121
http://cgasa.sbu.ac.ir/article_87116_929764e335e7d4c92a5611139b9e065a.pdf
dx.doi.org/10.29252/cgasa.12.1.89
Some aspects of cosheaves on diffeological spaces
Alireza
Ahmadi
Department of Math. Yazd University
Yazd, Iran
author
Akbar
Dehghan Nezhad
School of Mathematics, Iran University of Science and Technology,
Narmak,Tehran, 16846--13114, Iran
author
text
article
2020
eng
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.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
123
147
http://cgasa.sbu.ac.ir/article_87119_6b625005860bfe6a4bd5da17a099b89b.pdf
dx.doi.org/10.29252/cgasa.12.1.123
The notions of closedness and D-connectedness in quantale-valued approach spaces
Muhammad
Qasim
Department of Mathematics, School of Natural Sciences, National University of Sciences & Technology, Islamabad.
author
Samed
Ozkan
Department of Mathematics, Hacı Bektaş Veli University, Nevşehir, Turkey
author
text
article
2020
eng
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.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
149
173
http://cgasa.sbu.ac.ir/article_87411_0927cf623a93d8d592cac3c1677607b0.pdf
dx.doi.org/10.29252/cgasa.12.1.149
Classification of monoids by Condition $(PWP_{ssc})$
Pouyan
Khamechi
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
author
Hossein
Mohammadzadeh Saany
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
author
Leila
Nouri
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
author
text
article
2020
eng
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 $(PWP_{ssc})$.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
175
197
http://cgasa.sbu.ac.ir/article_85729_9d3888f3fd18b864c1967d267a21ae2c.pdf
dx.doi.org/10.29252/cgasa.12.1.175
Persian Abstracts, Vol. 11, No. 1.
text
article
2020
eng
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
12
v.
1
no.
2020
http://cgasa.sbu.ac.ir/article_87447_30e3ae686ac4b95893d47c5aff5815fc.pdf