$G$-Weights and $p$-Local Rank
P.
Manuel Dominguez Wade
Department of
Mathematics, Matanzas University, Matanzas, Cuba
author
text
article
2017
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
2
no.
2017
1
12
https://jart.guilan.ac.ir/article_2711_8f0e0342d1bad2b4ab66eb7767948d0e.pdf
dx.doi.org/10.22124/jart.2017.2711
On subalgebras of an evolution algebra of a "chicken" population
U.A.
Rozikov
Institute of Mathematics, Tashkent, Uzbekistan
author
B.A.
Omirov
Institute of Mathematics, Tashkent. Uzbekistan
author
text
article
2017
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
2
no.
2017
13
24
https://jart.guilan.ac.ir/article_2712_222c9e56b9aa274159d6c55d5619763d.pdf
dx.doi.org/10.22124/jart.2017.2712
Algebraic adjoint of the polynomials-polynomial matrix multiplication
R.
Andriamifidisoa
Department of Mathematics and Computer Science, University of Antananarivo, Antananarivo, Madagascar
author
H.
Randriambolasata
Department of
Mathematics and Computer Science, University
of Antananarivo, Antananarivo, Madagascar
author
text
article
2017
eng
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
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
2
no.
2017
25
33
https://jart.guilan.ac.ir/article_2713_513fa552e02ac910322e1193e698e82b.pdf
dx.doi.org/10.22124/jart.2017.2713
σ-sporadic prime ideals and superficial elements
D.
Kamano
D\'epartment de Sciences et Technologie, Section Math\'ematiques, Ecole normale sup\'erieure, Abidjan, C\^ote d'Ivoire
author
K.A.
Essan
UFR sciences sociales, Universit'e P'el'eforo Gon Coulibaly, Korhogo, C^ote d'Ivoire
author
A.
Abdoulaye
Laboratoire de
Math\'ematiques et Informatique, Universit\'e Nangui Abrogoua, Abidjan, C\^ote d'Ivoire
author
E.D.
Akeke
UFR de Math'ematiques et Informatique, Universit'e F'elix Houphouet Boigny, Abidjan, C^ote d'Ivoire
author
text
article
2017
eng
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 $f_I=(I^n)_{n\in\mathbb{N}}$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
2
no.
2017
35
45
https://jart.guilan.ac.ir/article_2714_3bb28c732e69e2ea353a223c92597da3.pdf
dx.doi.org/10.22124/jart.2017.2714
On the additive maps satisfying Skew-Engel conditions
M.
Nadeem
Department of
Mathematics, Government College University, Lahore, Pakistan
author
M.
Aslam
Department of
Mathematics, Government College University, Lahore, Pakistan
author
Y.
Ahmed
Department of
Mathematics, Government College University, Lahore, Pakistan
author
text
article
2017
eng
Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:I\rightarrow R$ 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 $f (x)=0$ $\forall\,x\in I$ provided $2\neq$ 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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
2
no.
2017
47
58
https://jart.guilan.ac.ir/article_2715_db25ae4c151c5a154173eaca9ba7e7fa.pdf
dx.doi.org/10.22124/jart.2017.2715
Self-cogenerator modules and their applications
Y.
Talebi
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
author
M.
Hosseinpour
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
author
text
article
2017
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
2
no.
2017
59
68
https://jart.guilan.ac.ir/article_2716_e72e91aabb355c0e3f819156779a3c44.pdf
dx.doi.org/10.22124/jart.2017.2716