2017
5
2
0
0
$G$Weights and $p$Local Rank
2
2
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.
1

1
12


P.
Manuel Dominguez Wade
Department of
Mathematics, Matanzas University, Matanzas, Cuba
Department of
Mathematics, Matanzas University,
Cuba
pedroalgebralineal@gmail.com
Radical vertex
$G$weight
$p$local rank
On subalgebras of an evolution algebra of a "chicken" population
2
2
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 lowdimensional EACP are obtained.
1

13
24


U.A.
Rozikov
Institute of Mathematics, Tashkent, Uzbekistan
Institute of Mathematics, Tashkent, Uzbekistan
Uzbekistan
rozikovu@yandex.ru


B.A.
Omirov
Institute of Mathematics, Tashkent. Uzbekistan
Institute of Mathematics, Tashkent. Uzbekistan
Uzbekistan
omirovb@mail.ru
Evolution algebra
bisexual population
associative algebra
subalgebra
Algebraic adjoint of the polynomialspolynomial matrix multiplication
2
2
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
1

25
33


R.
Andriamifidisoa
Department of Mathematics and Computer Science, University of Antananarivo, Antananarivo, Madagascar
Department of Mathematics and Computer Science,
Madagascar
rmw278@yahoo.fr


H.
Randriambolasata
Department of
Mathematics and Computer Science, University
of Antananarivo, Antananarivo, Madagascar
Department of
Mathematics and Computer Science,
Madagascar
sosorandriambolasata@gmail.com
Operator in the shifts
scalar product
algebraic adjoint
σsporadic prime ideals and superficial elements
2
2
Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semiprime 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 $f_I=(I^n)_{ninmathbb{N}}$.
1

35
45


D.
Kamano
D'epartment de Sciences et Technologie, Section Math'ematiques, Ecole normale sup'erieure, Abidjan, C^ote d'Ivoire
D'epartment de Sciences et Technologie,
Ivory Coast (Cote D''Ivoire)
kamanodamase@yahoo.fr


K.A.
Essan
UFR sciences sociales, Universit'e P'el'eforo Gon Coulibaly, Korhogo, C^ote d'Ivoire
UFR sciences sociales, Universit'e P'el&
Ivory Coast (Cote D''Ivoire)
ambroisessan@yahoo.fr


A.
Abdoulaye
Laboratoire de
Math'ematiques et Informatique, Universit'e Nangui Abrogoua, Abidjan, C^ote d'Ivoire
Laboratoire de
Math'ematiques et Informatiqu
Ivory Coast (Cote 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
UFR de Math'ematiques et Informatique,
Ivory Coast (Cote D''Ivoire)
ericdago@yahoo.fr
Noetherian ring
Filtration
semiprime operation
associated prime ideals
superficial elements
On the additive maps satisfying SkewEngel conditions
2
2
Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:Irightarrow R$ be an additivemap. Then skewEngel 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 MAsemirings.
1

47
58


M.
Nadeem
Department of
Mathematics, Government College University, Lahore, Pakistan
Department of
Mathematics, Government College
Pakistan
nadeemkasuri25@gmail.com


M.
Aslam
Department of
Mathematics, Government College University, Lahore, Pakistan
Department of
Mathematics, Government College
Pakistan
aslam298@gmail.com


Y.
Ahmed
Department of
Mathematics, Government College University, Lahore, Pakistan
Department of
Mathematics, Government College
Pakistan
yaqoubahmedkhan@gmail.com
Additive map
prime ring
semiprime ring
MAsemiring
Selfcogenerator modules and their applications
2
2
Let $R$ be a ring and $M$ be a right $R$module. In this paper, we give some properties of selfcogeneratormodules. If $M$ is selfcogenerator and $S = End_{R}(M)$ is a cononsingular ring, then $M$ is a$mathcal{K}$module. It is shown that every selfcogenerator Baer is dual Baer.
1

59
68


Y.
Talebi
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Mathematical
Iran
talebi@umz.ac.ir


M.
Hosseinpour
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Mathematical
Iran
mehrab.hosseinpour@gmail.com
Selfcogenerator modules
Baer rings and modules
dual Baer modules