University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
2
2017
12
01
$G$-Weights and $p$-Local Rank
1
12
EN
P.
Manuel Dominguez Wade
Department of
Mathematics, Matanzas University, Matanzas, Cuba
pedroalgebralineal@gmail.com
10.22124/jart.2017.2711
Let $k$ be field of characteristic $p$, andlet $G$ be any finite group with splitting field $k$. Assume that $B$ is a $p$-block of $G$.In this paper, we introduce the notion of radical $B$-chain $C_{B}$, and we show that the $p$-local rank of $B$ is equals the length of $C_{B}$. Moreover, we prove that the vertex of a simple $kG$-module $S$ is radical if and only if it has the same vertex of the unique direct summand, up to isomorphism, of the Sylow permutationmodule whose radical quotient is isomorphic to $S$. Finally, we prove the vertices of certain direct summands of the Sylow permutation module are bounds for the vertices of simple $kG$-modules.
Radical vertex,$G$-weight,$p$-local rank
https://jart.guilan.ac.ir/article_2711.html
https://jart.guilan.ac.ir/article_2711_8f0e0342d1bad2b4ab66eb7767948d0e.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
2
2017
12
01
On subalgebras of an evolution algebra of a "chicken" population
13
24
EN
U.A.
Rozikov
Institute of Mathematics, Tashkent, Uzbekistan
rozikovu@yandex.ru
B.A.
Omirov
Institute of Mathematics, Tashkent. Uzbekistan
omirovb@mail.ru
10.22124/jart.2017.2712
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. For such algebras in terms of its structure constants we calculate right and plenary periods of generator elements. Some results on subalgebras of EACP and ideals on low-dimensional EACP are obtained.
Evolution algebra,bisexual population,associative algebra,subalgebra
https://jart.guilan.ac.ir/article_2712.html
https://jart.guilan.ac.ir/article_2712_222c9e56b9aa274159d6c55d5619763d.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
2
2017
12
01
Algebraic adjoint of the polynomials-polynomial matrix multiplication
25
33
EN
R.
Andriamifidisoa
Department of Mathematics and Computer Science, University of Antananarivo, Antananarivo, Madagascar
rmw278@yahoo.fr
H.
Randriambolasata
Department of
Mathematics and Computer Science, University
of Antananarivo, Antananarivo, Madagascar
sosorandriambolasata@gmail.com
10.22124/jart.2017.2713
This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field
Operator in the shifts,scalar product,algebraic adjoint
https://jart.guilan.ac.ir/article_2713.html
https://jart.guilan.ac.ir/article_2713_513fa552e02ac910322e1193e698e82b.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
2
2017
12
01
σ-sporadic prime ideals and superficial elements
35
45
EN
D.
Kamano
D\'epartment de Sciences et Technologie, Section Math\'ematiques, Ecole normale sup\'erieure, Abidjan, C\^ote d'Ivoire
kamanodamase@yahoo.fr
K.A.
Essan
UFR sciences sociales, Universit'e P'el'eforo Gon Coulibaly, Korhogo, C^ote d'Ivoire
ambroisessan@yahoo.fr
A.
Abdoulaye
Laboratoire de
Math\'ematiques et Informatique, Universit\'e Nangui Abrogoua, Abidjan, C\^ote d'Ivoire
abdoulassan2002@yahoo.fr
E.D.
Akeke
UFR de Math'ematiques et Informatique, Universit'e F'elix Houphouet Boigny, Abidjan, C^ote d'Ivoire
ericdago@yahoo.fr
10.22124/jart.2017.2714
Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I)$, with $n$ small, which are the sets of $sigma$-sporadic prime divisors of $I$.We also give some relationships between $sigma(f_I)$-superficial elements and asymptotic prime $sigma$-divisors, where $sigma (f_I)$ is the $sigma$-closure of the $I$-adic filtration $f_I=(I^n)_{ninmathbb{N}}$.
Noetherian ring,Filtration,semi-prime operation,associated prime ideals,superficial elements
https://jart.guilan.ac.ir/article_2714.html
https://jart.guilan.ac.ir/article_2714_3bb28c732e69e2ea353a223c92597da3.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
2
2017
12
01
On the additive maps satisfying Skew-Engel conditions
47
58
EN
M.
Nadeem
Department of
Mathematics, Government College University, Lahore, Pakistan
nadeemkasuri25@gmail.com
M.
Aslam
Department of
Mathematics, Government College University, Lahore, Pakistan
aslam298@gmail.com
Y.
Ahmed
Department of
Mathematics, Government College University, Lahore, Pakistan
yaqoubahmedkhan@gmail.com
10.22124/jart.2017.2715
Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:Irightarrow R$ be an additivemap. Then skew-Engel condition $langle... langle langle$$f(x),x^{n_1} rangle,x^{n_2} rangle ,...,x^{n_k} rangle=0$ implies that $f (x)=0$ $forall,xin I$ provided $2neq$ char $(R)>n_1+n_2+...+n_k, $ where $n_1,n_2,...,n_k$ are natural numbers. This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.
Additive map,prime ring,semiprime ring,MA-semiring
https://jart.guilan.ac.ir/article_2715.html
https://jart.guilan.ac.ir/article_2715_db25ae4c151c5a154173eaca9ba7e7fa.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
2
2017
12
01
Self-cogenerator modules and their applications
59
68
EN
Y.
Talebi
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
talebi@umz.ac.ir
M.
Hosseinpour
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
mehrab.hosseinpour@gmail.com
10.22124/jart.2017.2716
Let $R$ be a ring and $M$ be a right $R$-module. In this paper, we give some properties of self-cogeneratormodules. If $M$ is self-cogenerator and $S = End_{R}(M)$ is a cononsingular ring, then $M$ is a$mathcal{K}$-module. It is shown that every self-cogenerator Baer is dual Baer.
Self-cogenerator modules,Baer rings and modules,dual Baer modules
https://jart.guilan.ac.ir/article_2716.html
https://jart.guilan.ac.ir/article_2716_e72e91aabb355c0e3f819156779a3c44.pdf