2024-03-29T05:46:05Z
https://as.yazd.ac.ir/?_action=export&rf=summon&issue=233
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2017
4
2
Results on Engel Fuzzy Subgroups
E.
Mohamadzadeh
R.A.
Borzouei
Young Bae
Jun
In the classical group theory there is an open question: Is every torsion free n-Engel group (for n ≥ 4), nilpotent?. To answer the question, Traustason [11] showed that with some additional conditions all 4-Engel groups are locally nilpotent. Here, we gave some partial answer to this question on Engel fuzzy subgroups. We show that if μ is a normal 4-Engel fuzzy subgroup of group G, x,y in G and a =yx, then μ|< a, y> is a generalized nilpotent of class at most 2. Also we define a torsion free fuzzy subgroup and show that if μ is a 4-Engel torsion free fuzzy subgroup of G, then μ|< a, y> is a generalized nilpotent of class at most 4, for conjugate elements a,y in G.
n-Engel group
(torsion free) n-Engle fuzzy subgroup
generalized nilpotent fuzzy subgroup
2017
11
01
1
14
https://as.yazd.ac.ir/article_1137_f2037c3d0ac22a236d52bb0d8f93c479.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2017
4
2
On the zero forcing number of some Cayley graphs
Ebrahim
Vatandoost
Yasser
Golkhandy Pour
Let Γa be a graph whose each vertex is colored either white or black. If u is a black vertex of Γ such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a Γ graph is a subset of vertices Z\subseteq V(Γ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the color of all vertices Γ in to black. The zero forcing number of Γ is the minimum of |Z| over all zero forcing sets for Γ and is denoted by Z(Γ). In this paper, we consider the zero forcing number of some families of Cayley graphs. In this regard, we show that Z(Cay(D2n,S))=2|S|-2, where D2n is dihedral group of order 2n and S={a, a3, ... , a2k-1, b}. Also, we obtain Z(Cay(G,S)), where G=< a> is a cyclic group of even order n and S={ai : 1≤ i≤ n and i is odd}, S={ai :1≤ i≤ n and i is odd}\{ak,a-k} or |S|=3.
Zero forcing number
Cayley graph
Algorithm
2017
11
01
15
25
https://as.yazd.ac.ir/article_1138_9db184354340daa957b1685cee808a44.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2017
4
2
On the eigenvalues of non-commuting graphs
Modjtaba
Ghorbani
Zahra
Gharavi
Ali
Zaeem-Bashi
The non-commuting graph $\Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(\Gamma(G))=G\setminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $\Gamma(G)$ if and only if $xy \neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.
non-commuting graph
characteristic polynomial
center of group
2017
11
01
27
38
https://as.yazd.ac.ir/article_1140_e297f9b440407c2805064ecd67cc316c.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2017
4
2
Note on regular and coregular sequences
Hero
Saremi
Let $R$ be a commutative Noetherian ring and let $M$ be a finitely generated $R$-module. If $I$ is an ideal of $R$ generated by $M$-regular sequence, then we study the vanishing of the first $\Tor$ functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the first $\Ext$ functors.
regular sequence
coregular sequence
ring
2017
11
01
39
43
https://as.yazd.ac.ir/article_1168_58cfce99b8ea661d8c252451867d7d7e.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2017
4
2
An Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves
Mojtaba
Bahramian
Khadijeh
Eslami
In a (t,n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logarithm problem (ECDLP) by using generalized Jacobian of elliptic curves. The proposed scheme has all the benefits of Shao and Cao, however, our scheme no need to a secure channel. Furthermore, we exploit the techniques via elliptic curves to perform the scheme. This can be very important because the hardness of discrete logarithm problem on elliptic curves increases security of the proposed scheme.
Secret Sharing
Elliptic Curves
Generalized Jacobians
2017
11
01
45
55
https://as.yazd.ac.ir/article_1169_52f01c3ebd1b9fca60c6e9f68a01edf4.pdf
Algebraic Structures and Their Applications
ASTA
2382-9761
2382-9761
2017
4
2
Applications of a group in general fuzzy automata
Mohammad
Horry
Let $\tilde{F}=(Q,\S,\tilde{R},Z,\omega,\tilde{\delta}, F_1,F_2)$ be a general fuzzy automaton and the set of its states be a group. The aim of this paper is the study of applications of a group in a general fuzzy automaton. For this purpose, we define the concepts of fuzzy normal kernel of a general fuzzy automaton, fuzzy kernel of a general fuzzy automaton, adjustable, multiplicative. Then we obtain the relationships between them.
Fuzzy automata
group
normal subgroup
fuzzy subgroup
fuzzy normal subgroup
2017
11
01
57
69
https://as.yazd.ac.ir/article_1170_4139753a3d6b4418249651a24aa57957.pdf