@article {
author = {},
title = {Cover for Vol. 8, No. 1.},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {88-88},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {.},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_55242.html},
eprint = {https://cgasa.sbu.ac.ir/article_55242_bc9bbc290cfae439827b4a9653667fce.pdf}
}
@article {
author = {Banaschewski, Bernhard},
title = {On the pointfree counterpart of the local definition of classical continuous maps},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {1-8},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.8.1.1},
abstract = {The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $\varphi_U: U \to Y$ on each member $U$ of an open cover ${\mathfrak C}$ of $X$ such that $\varphi_U\mid U \cap V = \varphi_V \mid U \cap V$ for all $U,V \in {\mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar classical counterpart concerning finite closed covers of a space $X$ (Picado and Pultr [4]). This note presents alternative proofs of these pointfree results which differ from those of [4] by treating the issue in terms of frame homomorphisms while the latter deals with the dual situation concerning localic maps. A notable advantage of the present approach is that it also provides proofs of the analogous results for some significant variants of frames which are not covered by the localic arguments.},
keywords = {Pointfree topology,continuous map,localic maps},
url = {https://cgasa.sbu.ac.ir/article_32712.html},
eprint = {https://cgasa.sbu.ac.ir/article_32712_7102051b8b0d2b0555b4ab6cee021fc7.pdf}
}
@article {
author = {Hadjirezaei, Somayeh and Karimzadeh, Somayeh},
title = {On finitely generated modules whose first nonzero Fitting ideals are regular},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {9-18},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.8.1.9},
abstract = {A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of $R^n$ which is generated by columns of a matrix $A=(a_{ij})$ with $a_{ij}\in R$ for all $1\leq i\leq n$, $j\in \Lambda$, where $\Lambda $ is a (possibly infinite) index set. Let $M=R^n/N$ be a module of type ($F_{n-1}$) and ${\rm T}(M)$ be the submodule of $M$ consisting of all elements of $M$ that are annihilated by a regular element of $R$. For $ \lambda\in \Lambda $, put $M_\lambda=R^n/<(a_{1\lambda},...,a_{n\lambda})^t>$. The main result of this paper asserts that if $M_\lambda $ is a regular $R$-module, for some $\lambda\in\Lambda$, then $M/{\rm T}(M)\cong M_\lambda/{\rm T}(M_\lambda)$. Also it is shown that if $M_\lambda$ is a regular torsionfree $R$-module, for some $\lambda\in \Lambda$, then $ M\cong M_\lambda. $ As a consequence we characterize all non-torsionfree modules over a regular ring, whose first nonzero Fitting ideals are maximal.},
keywords = {Fitting ideals,type of a module,torsion submodule},
url = {https://cgasa.sbu.ac.ir/article_33815.html},
eprint = {https://cgasa.sbu.ac.ir/article_33815_eb94849dbfc998e1f81615c7347eb37f.pdf}
}
@article {
author = {Abbad, Omar},
title = {Equivalences in Bicategories},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {19-33},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.8.1.19},
abstract = {In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In particular, all calculations done in a bicategory are fully explicit, in order to overcome the difficulties which arise when working with bicategories instead of 2-categories.},
keywords = {Equivalences,bicategories,1-cells equivalence},
url = {https://cgasa.sbu.ac.ir/article_39393.html},
eprint = {https://cgasa.sbu.ac.ir/article_39393_332fddb8a87abd60e8a8e0ea8a4acb90.pdf}
}
@article {
author = {Khosravi, Roghaieh and Liang, Xingliang},
title = {On (po-)torsion free and principally weakly (po-)flat $S$-posets},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {35-49},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.8.1.35},
abstract = {In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are weakly po-flat.},
keywords = {Torsion free,po-torsion free,principally weakly flat,pomonoid,$S$-poset},
url = {https://cgasa.sbu.ac.ir/article_44578.html},
eprint = {https://cgasa.sbu.ac.ir/article_44578_81b18d36c9840fe2d5160c1baf42be5a.pdf}
}
@article {
author = {Zou, Zhiwei and Li, Qingguo and Guo, Lankun},
title = {A note on the problem when FS-domains coincide with RB-domains},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {51-59},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.8.1.51},
abstract = {In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilattice is an FS-domain if and only if it is an RB-domain; an L-domain is an FS-domain if and only if it is an RB-domain. These results are expected to provide useful hints to the open problem of whether FS-domains are identical with RB-domains.},
keywords = {FS-domains,RB-domains,Super finitely separating functions,L-domains},
url = {https://cgasa.sbu.ac.ir/article_47217.html},
eprint = {https://cgasa.sbu.ac.ir/article_47217_df93e16f640375823b7ff13404710dde.pdf}
}
@article {
author = {Estaji, Ali Asghar and Hashemi, Ebrahim and Estaji, Ali Akbar},
title = {On Property (A) and the socle of the $f$-ring $Frm(\mathcal{P}(\mathbb R), L)$},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {61-80},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.8.1.61},
abstract = {For a frame $L$, consider the $f$-ring $ \mathcal{F}_{\mathcal P}L=Frm(\mathcal{P}(\mathbb R), L)$. In this paper, first we show that each minimal ideal of $ \mathcal{F}_{\mathcal P}L$ is a principal ideal generated by $f_a$, where $a$ is an atom of $L$. Then we show that if $L$ is an $\mathcal{F}_{\mathcal P}$-completely regular frame, then the socle of $ \mathcal{F}_{\mathcal P}L$ consists of those $f$ for which $coz (f)$ is a join of finitely many atoms. Also it is shown that not only $ \mathcal{F}_{\mathcal P}L$ has Property (A) but also if $L$ has a finite number of atoms then the residue class ring $ \mathcal{F}_{\mathcal P}L/\mathrm{Soc}( \mathcal{F}_{\mathcal P}L)$ has Property (A).},
keywords = {Minimal ideal,Socle,real-valued functions ring,ring with property $(A)$},
url = {https://cgasa.sbu.ac.ir/article_49786.html},
eprint = {https://cgasa.sbu.ac.ir/article_49786_0a546042fb7220c95d9b4ec558b5f554.pdf}
}
@article {
author = {},
title = {Persian Abstracts, Vol. 8.},
journal = {Categories and General Algebraic Structures with Applications},
volume = {8},
number = {1},
pages = {0-0},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {.},
keywords = {},
url = {https://cgasa.sbu.ac.ir/article_55243.html},
eprint = {https://cgasa.sbu.ac.ir/article_55243_cb399fe72fdc4e9d5798a1c46ba45fe5.pdf}
}