Characterization of $(\delta, \varepsilon)$-double derivation on rings and algebras
Z.
Jokar
Department of Mathematics, Mashhad Branch, Islamic Azad University-Mashhad, Iran
author
A.
Niknam
Department of Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University, Mashhad, Iran
author
text
article
2017
eng
This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $\mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, \delta, \varepsilon$ are additive mappings satisfying\begin{equation}d(x^n) = \sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+\sum^{n-1}_{j=1}\sum^{j}_{i=1}x^{n-1-j}\Big(\delta(x)x^{j-i}\varepsilon(x)+\varepsilon(x)x^{j-i}\delta(x)\Big)x^{i-1}\quad\end{equation}for all $x \in \mathcal{R}$. If $\delta(e) = \varepsilon(e) = 0$, then $d$ is a Jordan $(\delta, \varepsilon)$-double derivation. In particular, if $\mathcal{R}$ is a semiprime algebra and further, $\delta(x) \varepsilon(x) + \varepsilon(x) \delta(x) = \frac{1}{2}\Big[(\delta \varepsilon + \varepsilon \delta)(x^2) - (\delta \varepsilon(x) + \varepsilon \delta(x))x - x (\delta \varepsilon(x) + \varepsilon \delta(x))\Big]$ holds for all $x \in \mathcal{R}$, then $d - \frac{\delta \varepsilon + \varepsilon \delta}{2}$ is a derivation on $\mathcal{R}$.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
03
no.
2017
191
198
http://jlta.iauctb.ac.ir/article_536041_aedee60f073470d0b117dec680f647ff.pdf
Fuzzy almost generalized $e$-continuous mappings
A.
Vadivel
Department of Mathematics, Annamalai University, Annamalai Nagar, Chidambaram, India
author
B.
Vijayalakshmi
Department of Mathematics, Annamalai University, Annamalai Nagar, Chidambaram, India
author
text
article
2017
eng
In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{\frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and fuzzy generalized $e$-compact space. It is seen that a fuzzy almost generalized $e$-continuous mapping from a fuzzy $f T_{\frac{1}{2}}e$-space to another fuzzy topological space becomes fuzzy almost continuous mapping.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
03
no.
2017
199
206
http://jlta.iauctb.ac.ir/article_536043_7c95502bdd6dbd302abcc73a7c43fdb4.pdf
Spectral triples of weighted groups
M.
Amini
Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran
author
Kh.
Shamsolkotabi
Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran
author
text
article
2017
eng
We study spectral triples on (weighted) groups and consider functors between the categories of weighted groups and spectral triples. We study the properties of weights and the corresponding functor for spectral triples coming from discrete weighted groups.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
03
no.
2017
207
216
http://jlta.iauctb.ac.ir/article_535473_459ae47dbf75a963e1abf29ccf773a7f.pdf
On some Frobenius groups with the same prime graph as the almost simple group ${ {\bf PGL(2,49)}}$
A.
Mahmoudifar
Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran, Iran
author
text
article
2017
eng
The prime graph of a finite group $G$ is denoted by $\Gamma(G)$ whose vertex set is $\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $\Gamma(H)=\Gamma(G)$, in while $H\not\cong G$. In this paper, we consider finite groups with the same prime graph as the almost simple group $\textrm{PGL}(2,49)$. Moreover, we construct some Frobenius groups whose prime graphs coincide with $\Gamma(\textrm{PGL}(2,49))$, in particular, we get that $\textrm{PGL}(2,49)$ is unrecognizable by its prime graph.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
03
no.
2017
217
221
http://jlta.iauctb.ac.ir/article_536045_3d85a99b67d0a27c0d4b71dd3929b61e.pdf
Interval valued fuzzy weak bi-ideals of $\Gamma$-near-rings
V.
Chinnadurai
Department of Mathematics, Annamalai University, Annamalainagar-608 002, India
author
K.
Arulmozhi
Department of Mathematics, Annamalai University, Annamalainagar-608 002, India
author
S.
Kadalarasi
Department of Mathematics, Annamalai University, Annamalainagar-608 002, India
author
text
article
2017
eng
In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $\Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $\Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $\Gamma$-near-rings.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
03
no.
2017
223
236
http://jlta.iauctb.ac.ir/article_536046_58c0e14373c1b677c32ee78eaa568fea.pdf
Numerical solution of a system of fuzzy polynomial equations by modified Adomian decomposition method
M.
Mosleh
Department of Mathematics, Islamic Azad University, Firoozkooh Branch, Firoozkooh, Iran
author
text
article
2017
eng
In this paper, we present some efficient numerical algorithm for solving system of fuzzy polynomial equations based on Newton's method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
03
no.
2017
237
250
http://jlta.iauctb.ac.ir/article_533329_b24e6cc5af50a208735f84fbe9de87fd.pdf
Fixed point theory in generalized orthogonal metric space
M.
Eshaghi Gordji
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
author
H.
Habibi
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
author
text
article
2017
eng
In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
03
no.
2017
251
260
http://jlta.iauctb.ac.ir/article_533328_9d7078d29a5d86c4c5315da8f03e673b.pdf