2018-12-11T05:54:09Z
https://jart.guilan.ac.ir/?_action=export&rf=summon&issue=446
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
2
$G$-Weights and $p$-Local Rank
P.
Manuel Dominguez Wade
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
2017
12
01
1
12
https://jart.guilan.ac.ir/article_2711_8f0e0342d1bad2b4ab66eb7767948d0e.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
2
On subalgebras of an evolution algebra of a "chicken" population
U.A.
Rozikov
B.A.
Omirov
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
2017
12
01
13
24
https://jart.guilan.ac.ir/article_2712_222c9e56b9aa274159d6c55d5619763d.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
2
Algebraic adjoint of the polynomials-polynomial matrix multiplication
R.
Andriamifidisoa
H.
Randriambolasata
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
2017
12
01
25
33
https://jart.guilan.ac.ir/article_2713_513fa552e02ac910322e1193e698e82b.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
2
σ-sporadic prime ideals and superficial elements
D.
Kamano
K.A.
Essan
A.
Abdoulaye
E.D.
Akeke
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
2017
12
01
35
45
https://jart.guilan.ac.ir/article_2714_3bb28c732e69e2ea353a223c92597da3.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
2
On the additive maps satisfying Skew-Engel conditions
M.
Nadeem
M.
Aslam
Y.
Ahmed
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
2017
12
01
47
58
https://jart.guilan.ac.ir/article_2715_db25ae4c151c5a154173eaca9ba7e7fa.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
2
Self-cogenerator modules and their applications
Y.
Talebi
M.
Hosseinpour
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
2017
12
01
59
68
https://jart.guilan.ac.ir/article_2716_e72e91aabb355c0e3f819156779a3c44.pdf