Derivations in semiprime rings and Banach algebras
Sh.
Sahebi
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
P. O. Box 14168-94351, Tehran, Iran
author
V.
Rahmani
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
P. O. Box 14168-94351, Tehran, Iran
author
text
article
2013
eng
Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,y\in R$ where $0\neq b\in R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. We also obtain some related result in case $R$ is a non-commutative Banach algebra and d continuous or spectrally bounded.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
02
v.
03
no.
2013
129
135
http://jlta.iauctb.ac.ir/article_510014_c0ecf3a2d537d24ca2b30bd50175a60b.pdf
Some results of semilocally simply connected property
A.
Etemad Dehkordya
Department of Mathematical sciences, Isfahan University of Technology, Isfahan, Iran
author
M.
Malek Mohamad
Department of Mathematical sciences, Isfahan University of Technology, Isfahan, Iran
author
text
article
2013
eng
If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
02
v.
03
no.
2013
137
143
http://jlta.iauctb.ac.ir/article_510015_5062cb9c7c690e38b9dca1a0455c2dff.pdf
A generalization of Bertrand's test
A. A.
Tabatabai Adnani
Islamic Azad University, Central Tehran Branch, Tehran, Iran
author
A.
Reza
Islamic Azad University, Central Tehran Branch, Tehran, Iran
author
M.
Morovati
School of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran
author
text
article
2013
eng
One of the most practical routine tests for convergence of a positive series makes use of the ratio test. If this test fails, we can use Rabbe's test. When Rabbe's test fails the next sharper criteria which may sometimes be used is the Bertrand's test. If this test fails, we can use a generalization of Bertrand's test and such tests can be continued innitely. For simplicity, we call ratio test, Rabbe's test, Bertrand's test as the Bertrand's test of order 0, 1 and 2, respectively. In this paper, we generalize Bertrand's test in order k for natural k > 2. It is also shown that for any k, there exists a series such that the Bertrand's test of order fails, but such test of order k + 1 is useful, furthermore we show that there exists a series such that for any k, Bertrand's test of order k fails. The only prerequisite for reading this article is a standard knowledge of advanced calculus.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
02
v.
03
no.
2013
145
151
http://jlta.iauctb.ac.ir/article_510016_819b520d1a7e6d00b75db94497f5b7f8.pdf
On the Finite Groupoid G(n)
M.
Azadi
Department of Mathematics, Islamic Azad University, Centeral Tehran Branch, Tehran, Iran
author
H.
Amadi
Department of Mathematics, Islamic Azad University, Centeral Tehran Branch, Tehran, Iran
author
text
article
2013
eng
In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) to be commuting regular.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
02
v.
03
no.
2013
153
159
http://jlta.iauctb.ac.ir/article_510017_fb1252dd8598780a6b0d040a37bee02a.pdf
OD-characterization of $S_4(4)$ and its group of automorphisms
P.
Nosratpour
Department of mathematics, Ilam Branch, Islamic Azad university, Ilam, Iran
author
text
article
2013
eng
Let $G$ be a finite group and $\pi(G)$ be the set of all prime divisors of $|G|$. The prime graph of $G$ is a simple graph $\Gamma(G)$ with vertex set $\pi(G)$ and two distinct vertices $p$ and $q$ in $\pi(G)$ are adjacent by an edge if an only if $G$ has an element of order $pq$. In this case, we write $p\sim q$. Let $|G= p_1^{\alpha_1}\cdot p_2^{\alpha_2}\cdots p_k^{\alpha_k}$, where $p_1<p_2 <\dots < p_k$ are primes. For $p\in \pi(G)$, let $deg(p) = |\{q\in \pi(G)|p\sim q\}|$ be the degree of $p$ in the graph $\Gamma(G)$, we define $D(G)=(deg(p_1),deg(p_2),\dots,deg(p_k))$ and call it the degree pattern of $G$. A group $G$ is called $k$-fold OD characterizable if there exist exactly $k$ non-isomorphic groups $S$ such that $|G|=|S|$ and $D(G) = D(S)$. Moreover, a 1-fold OD-characterizable group is simply called an OD-characterizable group. Let $L = S_4(4)$ be the projective symplectic group in dimension 4 over a field with 4 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to L. Since $Aut(L)\equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
02
v.
03
no.
2013
161
166
http://jlta.iauctb.ac.ir/article_510018_04b780588dcc071ae9418ffe0226bd47.pdf
On the nonnegative inverse eigenvalue problem of traditional matrices
A. M.
Nazari
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
author
S.
Kamali Maher
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
author
text
article
2013
eng
In this paper, at first for a given set of real or complex numbers $\sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $\sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
02
v.
03
no.
2013
167
174
http://jlta.iauctb.ac.ir/article_510019_85f53f76519a196781fdc2d15d2801fc.pdf
Some properties of band matrix and its application to the numerical solution one-dimensional Bratu's problem
R.
Jalilian
Department of Mathematics, Razi University Tagh Bostan, Kermanshah P.O. Box 6714967346 Iran
author
Y.
Jalilian
Department of Mathematics, Razi University Tagh Bostan, Kermanshah P.O. Box 6714967346 Iran
author
H.
Jalilian
School of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran
author
text
article
2013
eng
A Class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Associated boundary formulas are developed. Convergence analysis of these methods is discussed. Numerical results are given to illustrate the efficiency of methods.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
02
v.
03
no.
2013
175
189
http://jlta.iauctb.ac.ir/article_510020_df91852bd2fbf4c39cb43b01bc47efbb.pdf