@article {
author = {},
title = {Cover for Vol. 12, No. 1.},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {-},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_87446.html},
eprint = {https://cgasa.sbu.ac.ir/article_87446_a7e000c9d66011a5abdb6400f8446452.pdf}
}
@article {
author = {Gladki, Pawel and Worytkiewicz, Krzysztof},
title = {Witt rings of quadratically presentable fields},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {1-23},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.1},
abstract = {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.},
keywords = {Quadratically presentable fields,Witt rings,hyperfields,quadratic forms},
url = {https://cgasa.sbu.ac.ir/article_87412.html},
eprint = {https://cgasa.sbu.ac.ir/article_87412_e4ca569b071e83128b5db22ac6d06101.pdf}
}
@article {
author = {Rashidi, Hamideh and Golchin, Akbar and Mohammadzadeh Saany, Hossein},
title = {On $GPW$-Flat Acts},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {25-42},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.25},
abstract = {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.},
keywords = {$GPW$-flat,Eventually regular monoid,Eventually left almost regular monoid},
url = {https://cgasa.sbu.ac.ir/article_82637.html},
eprint = {https://cgasa.sbu.ac.ir/article_82637_db225e4212ba0171013678302be2c9d2.pdf}
}
@article {
author = {Mahboob, Ahsan and Khan, Noor and Davvaz, Bijan},
title = {$(m,n)$-Hyperideals in Ordered Semihypergroups},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {43-67},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.43},
abstract = {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.},
keywords = {Ordered semihypergroups,$(m,0)$-hyperideals,$(0,n)$-hyperideals},
url = {https://cgasa.sbu.ac.ir/article_87415.html},
eprint = {https://cgasa.sbu.ac.ir/article_87415_1fd525cccd124d58a33309087242f95f.pdf}
}
@article {
author = {Jafarzadeh, Najmeh and Ameri, Reza},
title = {On exact category of $(m, n)$-ary hypermodules},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {69-88},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.69},
abstract = {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.},
keywords = {$(m,n)$-hypermodules,kernel,cokernel,balanced category,fundamental functor,exact category},
url = {https://cgasa.sbu.ac.ir/article_80792.html},
eprint = {https://cgasa.sbu.ac.ir/article_80792_907e526521584c03372aaada0e600e45.pdf}
}
@article {
author = {Grandis, Marco and Janelidze, George},
title = {From torsion theories to closure operators and factorization systems},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {89-121},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.89},
abstract = {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].},
keywords = {Exact sequence,torsion theory,closure operator,factorization system,ideal of null morphisms},
url = {https://cgasa.sbu.ac.ir/article_87116.html},
eprint = {https://cgasa.sbu.ac.ir/article_87116_929764e335e7d4c92a5611139b9e065a.pdf}
}
@article {
author = {Ahmadi, Alireza and Dehghan Nezhad, Akbar},
title = {Some aspects of cosheaves on diffeological spaces},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {123-147},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.123},
abstract = {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.},
keywords = {Cosheaves,quasi-cosheaves,site of plots,covering generating families,quasi-v{C}ech homology,diffeological spaces},
url = {https://cgasa.sbu.ac.ir/article_87119.html},
eprint = {https://cgasa.sbu.ac.ir/article_87119_6b625005860bfe6a4bd5da17a099b89b.pdf}
}
@article {
author = {Qasim, Muhammad and Ozkan, Samed},
title = {The notions of closedness and D-connectedness in quantale-valued approach spaces},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {149-173},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.149},
abstract = {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.},
keywords = {$mathcal{L}$-approach distance space,$mathcal{L}$-gauge space,topological category,Separation,closedness,D-connectedness},
url = {https://cgasa.sbu.ac.ir/article_87411.html},
eprint = {https://cgasa.sbu.ac.ir/article_87411_0927cf623a93d8d592cac3c1677607b0.pdf}
}
@article {
author = {Khamechi, Pouyan and Mohammadzadeh Saany, Hossein and Nouri, Leila},
title = {Classification of monoids by Condition $(PWP_{ssc})$},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {175-197},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.175},
abstract = {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 $(PWP_{ssc})$.},
keywords = {$S$-act,Flatness properties,Condition $(PWP_{ssc})$,semi-cancellative,$e$-cancellative},
url = {https://cgasa.sbu.ac.ir/article_85729.html},
eprint = {https://cgasa.sbu.ac.ir/article_85729_9d3888f3fd18b864c1967d267a21ae2c.pdf}
}
@article {
author = {},
title = {Persian Abstracts, Vol. 11, No. 1.},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {-},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_87447.html},
eprint = {https://cgasa.sbu.ac.ir/article_87447_30e3ae686ac4b95893d47c5aff5815fc.pdf}
}