HX-hypergroups associated with the direct products of some ${\bf Z}/n {\bf Z}$
Piergiulio
Corsini
University of Udine
author
text
article
2016
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
1
no.
2016
1
15
http://as.yazd.ac.ir/article_835_1f23c85a508ef75b7ad85d4301624c32.pdf
A note on the order graph of a group
Hamid Reza
Dorbidi
University of Jiroft
author
text
article
2016
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
1
no.
2016
17
24
http://as.yazd.ac.ir/article_875_0edfd6e49270d69dbf1f6ea8948e0b59.pdf
Exact sequences of extended $d$-homology
Mohammad Zaher
Kazemi Baneh
University of Kurdistan
author
Seyed Naser
Hosseini
Shahid Bahonar University of Kerman
author
text
article
2016
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
1
no.
2016
25
38
http://as.yazd.ac.ir/article_886_e041c7772dac1fb8eb2e2a396ea1a011.pdf
The principal ideal subgraph of the annihilating-ideal graph of commutative rings
Reza
Taheri
Islamic Azad University, Science and Research Branch, Tehran, Iran
author
Abolfazl
Tehranian
Islamic Azad University, Science and Research Branch, Tehran, Iran
author
text
article
2016
eng
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 $\mathbb{AG}_s(R)$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
1
no.
2016
39
52
http://as.yazd.ac.ir/article_888_2d482e44ddd64c95a532eea7ca73b7f8.pdf
The concept of logic entropy on D-posets
Uosef
Mohammadi
University of Jiroft
author
text
article
2016
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
3
v.
1
no.
2016
53
61
http://as.yazd.ac.ir/article_900_22873ec50d4c1ad74a344a74ff1e040d.pdf