Central Tehran Branch, Islamic Azad University
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
02
03
2013
09
01
Derivations in semiprime rings and Banach algebras
129
135
EN
Sh.
Sahebi
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
P. O. Box 14168-94351, Tehran, Iran
V.
Rahmani
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
P. O. Box 14168-94351, Tehran, Iran
venosrahmani@yahoo.com
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 $x,yin R$ where $0neq bin R$, 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.
prime ring,semiprime ring,derivation,Utumi quotient ring,Banach algebra
http://jlta.iauctb.ac.ir/article_510014.html
http://jlta.iauctb.ac.ir/article_510014_c0ecf3a2d537d24ca2b30bd50175a60b.pdf
Central Tehran Branch, Islamic Azad University
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
02
03
2013
09
01
Some results of semilocally simply connected property
137
143
EN
A.
Etemad Dehkordya
Department of Mathematical sciences, Isfahan University of Technology, Isfahan, Iran
ae110mat@cc.iut.ac.ir
M.
Malek Mohamad
Department of Mathematical sciences, Isfahan University of Technology, Isfahan, Iran
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.
Semilocally simply connected,topological fundamental group,discrete space
http://jlta.iauctb.ac.ir/article_510015.html
http://jlta.iauctb.ac.ir/article_510015_5062cb9c7c690e38b9dca1a0455c2dff.pdf
Central Tehran Branch, Islamic Azad University
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
02
03
2013
09
01
A generalization of Bertrand's test
145
151
EN
A. A.
Tabatabai Adnani
Islamic Azad University, Central Tehran Branch, Tehran, Iran
a.t.adnani@gmail.com
A.
Reza
Islamic Azad University, Central Tehran Branch, Tehran, Iran
M.
Morovati
School of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran
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.
Bertrand's test,Convergence test,Series test
http://jlta.iauctb.ac.ir/article_510016.html
http://jlta.iauctb.ac.ir/article_510016_819b520d1a7e6d00b75db94497f5b7f8.pdf
Central Tehran Branch, Islamic Azad University
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
02
03
2013
09
01
On the Finite Groupoid G(n)
153
159
EN
M.
Azadi
Department of Mathematics, Islamic Azad University, Centeral Tehran Branch, Tehran, Iran
meh.azadi@iauctb.ac.ir
H.
Amadi
Department of Mathematics, Islamic Azad University, Centeral Tehran Branch, Tehran, Iran
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.
Commuting regular semigroup,semigroup,groupoid
http://jlta.iauctb.ac.ir/article_510017.html
http://jlta.iauctb.ac.ir/article_510017_fb1252dd8598780a6b0d040a37bee02a.pdf
Central Tehran Branch, Islamic Azad University
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
02
03
2013
09
01
OD-characterization of $S_4(4)$ and its group of automorphisms
161
166
EN
P.
Nosratpour
Department of mathematics, Ilam Branch, Islamic Azad university, Ilam, Iran
p.nosratpour@ilam-iau.ac.ir
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 $psim q$. 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 $pin pi(G)$, let $deg(p) = |{qin pi(G)|psim q}|$ 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.
Finite simple group,OD-characterization,group of lie type
http://jlta.iauctb.ac.ir/article_510018.html
http://jlta.iauctb.ac.ir/article_510018_04b780588dcc071ae9418ffe0226bd47.pdf
Central Tehran Branch, Islamic Azad University
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
02
03
2013
09
01
On the nonnegative inverse eigenvalue problem of traditional matrices
167
174
EN
A. M.
Nazari
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
a-nazari@araku.ac.ir
S.
Kamali Maher
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
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.
Inverse eigenvalue problem,Tridiagonal matrix,Nonnegative matrix
http://jlta.iauctb.ac.ir/article_510019.html
http://jlta.iauctb.ac.ir/article_510019_85f53f76519a196781fdc2d15d2801fc.pdf
Central Tehran Branch, Islamic Azad University
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
02
03
2013
09
01
Some properties of band matrix and its application to the numerical solution one-dimensional Bratu's problem
175
189
EN
R.
Jalilian
Department of Mathematics, Razi University Tagh Bostan, Kermanshah P.O. Box 6714967346 Iran
rezajalilian@iust.ac.ir
Y.
Jalilian
Department of Mathematics, Razi University Tagh Bostan, Kermanshah P.O. Box 6714967346 Iran
H.
Jalilian
School of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran
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.
Two-point boundary value problem,Non-polynomial spline,Convergence analysis,Bratu's problem
http://jlta.iauctb.ac.ir/article_510020.html
http://jlta.iauctb.ac.ir/article_510020_df91852bd2fbf4c39cb43b01bc47efbb.pdf