2021-07-26T06:12:45Z
https://cgasa.sbu.ac.ir/?_action=export&rf=summon&issue=6846
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
Cover for Vol. 8, No. 1.
.
2018
01
01
88
88
https://cgasa.sbu.ac.ir/article_55242_bc9bbc290cfae439827b4a9653667fce.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
On the pointfree counterpart of the local definition of classical continuous maps
Bernhard
Banaschewski
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.
Pointfree topology
continuous map
localic maps
2018
01
01
1
8
https://cgasa.sbu.ac.ir/article_32712_7102051b8b0d2b0555b4ab6cee021fc7.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
On finitely generated modules whose first nonzero Fitting ideals are regular
Somayeh
Hadjirezaei
Somayeh
Karimzadeh
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.
Fitting ideals
type of a module
torsion submodule
2018
01
01
9
18
https://cgasa.sbu.ac.ir/article_33815_eb94849dbfc998e1f81615c7347eb37f.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
Equivalences in Bicategories
Omar
Abbad
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.
Equivalences
bicategories
1-cells equivalence
2018
01
01
19
33
https://cgasa.sbu.ac.ir/article_39393_332fddb8a87abd60e8a8e0ea8a4acb90.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
On (po-)torsion free and principally weakly (po-)flat $S$-posets
Roghaieh
Khosravi
Xingliang
Liang
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.
Torsion free
po-torsion free
principally weakly flat
pomonoid
$S$-poset
2018
01
01
35
49
https://cgasa.sbu.ac.ir/article_44578_81b18d36c9840fe2d5160c1baf42be5a.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
A note on the problem when FS-domains coincide with RB-domains
Zhiwei
Zou
Qingguo
Li
Lankun
Guo
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.
FS-domains
RB-domains
Super finitely separating functions
L-domains
2018
01
01
51
59
https://cgasa.sbu.ac.ir/article_47217_df93e16f640375823b7ff13404710dde.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
On Property (A) and the socle of the $f$-ring $Frm(mathcal{P}(mathbb R), L)$
Ali Asghar
Estaji
Ebrahim
Hashemi
Ali Akbar
Estaji
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).
Minimal ideal
Socle
real-valued functions ring
ring with property $(A)$
2018
01
01
61
80
https://cgasa.sbu.ac.ir/article_49786_0a546042fb7220c95d9b4ec558b5f554.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2018
8
1
Persian Abstracts, Vol. 8.
.
2018
01
01
0
0
https://cgasa.sbu.ac.ir/article_55243_cb399fe72fdc4e9d5798a1c46ba45fe5.pdf