@Article{ManuelDominguezWade2017,
author="Manuel Dominguez Wade, P.",
title="$G$-Weights and $p$-Local Rank",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="2",
pages="1-12",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2711",
url="http://jart.guilan.ac.ir/article_2711.html"
}
@Article{Rozikov2017,
author="Rozikov, U.A.
and Omirov, B.A.",
title="On subalgebras of an evolution algebra of a "chicken" population",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="2",
pages="13-24",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2712",
url="http://jart.guilan.ac.ir/article_2712.html"
}
@Article{Andriamifidisoa2017,
author="Andriamifidisoa, R.
and Randriambolasata, H.",
title="Algebraic adjoint of the polynomials-polynomial matrix multiplication",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="2",
pages="25-33",
abstract="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",
issn="2345-3931",
doi="10.22124/jart.2017.2713",
url="http://jart.guilan.ac.ir/article_2713.html"
}
@Article{Kamano2017,
author="Kamano, D.
and Essan, K.A.
and Abdoulaye, A.
and Akeke, E.D.",
title="σ-sporadic prime ideals and superficial elements",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="2",
pages="35-45",
abstract="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 $f_I=(I^n)_{n\in\mathbb{N}}$.",
issn="2345-3931",
doi="10.22124/jart.2017.2714",
url="http://jart.guilan.ac.ir/article_2714.html"
}
@Article{Nadeem2017,
author="Nadeem, M.
and Aslam, M.
and Ahmed, Y.",
title="On the additive maps satisfying Skew-Engel conditions",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="2",
pages="47-58",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2715",
url="http://jart.guilan.ac.ir/article_2715.html"
}
@Article{Talebi2017,
author="Talebi, Y.
and Hosseinpour, M.",
title="Self-cogenerator modules and their applications",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="2",
pages="59-68",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2716",
url="http://jart.guilan.ac.ir/article_2716.html"
}