Yazd University
Algebraic Structures and Their Applications
2382-9761
3
1
2016
02
01
HX-hypergroups associated with the direct products of some ${bf Z}/n {bf Z}$
1
15
EN
Piergiulio
Corsini
University of Udine
One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${bf Z}/n {bf Z},$ calculating their fuzzy grades.
$HX$-group,Fuzzy grade
http://as.yazd.ac.ir/article_835.html
http://as.yazd.ac.ir/article_835_1f23c85a508ef75b7ad85d4301624c32.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
3
1
2016
02
01
A note on the order graph of a group
17
24
EN
Hamid Reza
Dorbidi
University of Jiroft
hr_dorbidi@yahoo.com
The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
Connected graph,Frobenius group,Order graph,Prime graph
http://as.yazd.ac.ir/article_875.html
http://as.yazd.ac.ir/article_875_0edfd6e49270d69dbf1f6ea8948e0b59.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
3
1
2016
02
01
Exact sequences of extended $d$-homology
25
38
EN
Mohammad Zaher
Kazemi Baneh
University of Kurdistan
zaherkazemi@uok.ac.ir
Seyed Naser
Hosseini
Shahid Bahonar University of Kerman
nhoseini@uk.ac.ir
In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.
kernel,image,abelian category,standard homology,(extended) d-homology,exact sequence
http://as.yazd.ac.ir/article_886.html
http://as.yazd.ac.ir/article_886_e041c7772dac1fb8eb2e2a396ea1a011.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
3
1
2016
02
01
The principal ideal subgraph of the annihilating-ideal graph of commutative rings
39
52
EN
Reza
Taheri
Islamic Azad University, Science and Research Branch, Tehran, Iran
Abolfazl
Tehranian
Islamic Azad University, Science and Research Branch, Tehran, Iran
tehranian1340@yahoo.com
Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where $mathbb{P}(R)$ is the set of proper principal ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=(0)$. Then, we study some basic properties of $mathbb{AG}_P(R)$. For instance, we characterize rings for which $mathbb{AG}_P(R)$ is finite graph, complete graph, bipartite graph or star graph. Also, we study diameter and girth of $mathbb{AG}_P(R)$. Finally, we compare the principal ideal subgraph $mathbb{AG}_P(R)$ and spectrum subgraph $mathbb{AG}_s(R)$.
commutative rings,annihilating-ideal,principal ideal,graph
http://as.yazd.ac.ir/article_888.html
http://as.yazd.ac.ir/article_888_2d482e44ddd64c95a532eea7ca73b7f8.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
3
1
2016
02
01
The concept of logic entropy on D-posets
53
61
EN
Uosef
Mohammadi
University of Jiroft
u.mohamadi@ujiroft.ac.ir
In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied. The invariance of the {it logic entropy} of a system under isomorphism is proved. At the end, the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolmogorov-Sinai theorem is given.
D-poset,logic entropy,dynamical system,isomorphism,$ m $-generator
http://as.yazd.ac.ir/article_900.html
http://as.yazd.ac.ir/article_900_22873ec50d4c1ad74a344a74ff1e040d.pdf