Journal Cover of "Categories and General Algebraic Structures with Applications"
text
article
2016
eng
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
http://www.cgasa.ir/article_13487_06c4af7ef944bbe97b5200a846968195.pdf
Birkhoff's Theorem from a geometric perspective: A simple example
F. William
Lawvere
Department of Mathematics, University at Buffalo, Buffalo, New York 14260-2900, United States of America.
author
text
article
2016
eng
From Hilbert's theorem of zeroes, and from Noether's ideal theory, Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple example that illustrates some of the aspects of this relationship. The dualization from algebra to geometry in the basic Grothendieck spirit can be accomplished (without intervention of topological spaces) by the following method, known as Isbell conjugacy.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
1
8
http://www.cgasa.ir/article_12425_b4ce2ab0ae3a843f00ff011b054f918b.pdf
Steps toward the weak higher category of weak higher categories in the globular setting
Camell
Kachour
Department of Mathematics, Macquarie University, North Ryde, NSW 2109, Australia.
author
text
article
2016
eng
We start this article by rebuilding higher operads of weak higher transformations, and correct those in \cite{Cambat}. As in \cite{Cambat} we propose an operadic approach for weak higher $n$-transformations, for each $n\in\mathbb{N}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. The last chapter of this article asserts that, up to precise hypotheses, the higher operad $B^{0}_{C}$ of Batanin and the terminal higher operad $B^{0}_{S_{u}}$, both have the fractal property. In other words we isolate the precise technical difficulties behind a major problem in globular higher category theory, namely, that of proving the existence of the globular weak higher category of globular weak higher categories.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
9
42
http://www.cgasa.ir/article_11180_b13cacfd9afe5780932141c269d0add6.pdf
Basic notions and properties of ordered semihyperrings
B.
Davvaz
Department of
Mathematics, Yazd University, Yazd, Iran.
author
S.
Omidi
Department of
Mathematics, Yazd University, Yazd, Iran.
author
text
article
2016
eng
In this paper, we introduce the concept of semihyperring $(R,+,\cdot)$ together with a suitable partial order $\le$. Moreover, we introduce and study hyperideals in ordered semihyperrings. Simple ordered semihyperrings are defined and its characterizations are obtained. Finally, we study some properties of quasi-simple and $B$-simple ordered semihyperrings.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
43
62
http://www.cgasa.ir/article_11181_a73c9c7bbdb038f75ed62901bc042c2a.pdf
A characterization of finitely generated multiplication modules
Somayeh
Karimzadeh
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
author
Somayeh
Hadjirezaei
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
author
text
article
2016
eng
Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals of modules which are the direct sum of finitely generated module and finitely generated multiplication module are shown. Finally, we study some properties of modules that are the direct sum of multiplication modules in terms of Fitting ideals.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
63
74
http://www.cgasa.ir/article_12667_7069a62adca415a4a7178c2d5b4804a7.pdf
The ring of real-continuous functions on a topoframe
Ali Akbar
Estaji
Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
author
Abolghasem
Karimi Feizabadi
Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.
author
Mohammad
Zarghani
Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
author
text
article
2016
eng
A topoframe, denoted by $L_{ \tau}$, is a pair $(L, \tau)$ consisting of a frame $L$ and a subframe $ \tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $\tau $-real-continuous function on a frame $L$ and the set of real continuous functions $\mathcal{R}L_\tau $ as an $f$-ring. We show that $\mathcal{R}L_{ \tau}$ is actually a generalization of the ring $C(X)$ of all real-valued continuous functions on a completely regular Hausdorff space $X$. In addition, we show that $\mathcal{R}L_{ \tau}$ is isomorphic to a sub-$f$-ring of $\mathcal{R}\tau .$ Let ${\tau}$ be a topoframe on a frame $L$. The frame map $\alpha\in\mathcal{R}\tau $ is called $L$-{\it extendable} real continuous function if and only if for every $r\in \mathbb{R}$, $\bigvee^{L}_{r\in \mathbb R} (\alpha(-,r)\vee\alpha(r,-))'=\top.$ Finally, we prove that $\mathcal{R}^{L}{\tau}\cong \mathcal{R}L_{\tau}$ as $f$-rings, where $\mathcal{R}^{L}{\tau}$ is the set all of $L$-extendable real continuous functions of $ \mathcal{R}\tau $.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
75
94
http://www.cgasa.ir/article_13184_2f80da4a155068ca432d536a7217a6ab.pdf
On zero divisor graph of unique product monoid rings over Noetherian reversible ring
Ebrahim
Hashemi
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran, P.O. Box: 316-3619995161.
author
Abdollah
Alhevaz
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran, P.O. Box: 316-3619995161.
author
Eshag
Yoonesian
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran, P.O. Box: 316-3619995161.
author
text
article
2016
eng
Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is the graph whose vertices are the non-zero zero-divisors of $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$. In this paper, we bring some results about undirected zero-divisor graph of a monoid ring over reversible right (or left) Noetherian ring $R$. We essentially classify the diameter-structure of this graph and show that $0\leq \mbox{diam}(\Gamma(R))\leq \mbox{diam}(\Gamma(R[M]))\leq 3$. Moreover, we give a characterization for the possible diam$(\Gamma(R))$ and diam$(\Gamma(R[M]))$, when $R$ is a reversible Noetherian ring and $M$ is a u.p.-monoid. Also, we study relations between the girth of $\Gamma(R)$ and that of $\Gamma(R[M])$.
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
95
114
http://www.cgasa.ir/article_13185_9afc1a95b9340cdc8d14a1cee3b2fe5c.pdf
Vol. 4, Abstracts in Persian
text
article
2016
eng
چکیده مقالهها به زبانی فارسی
ساختارهای کلی جبری با کاربردها
جلد چهارم
Vol. 4 Abstracts in Persian
رستهها
م
Categories and General Algebraic Structures with Applications
Shahid Beheshti University
2345-5853
4
v.
1
no.
2016
121
130
http://www.cgasa.ir/article_13486_b4a9e871a6e3e022cdd05c3d87f7f635.pdf