University of GuilanJournal of Algebra and Related Topics2345-39315220171201$G$-Weights and $p$-Local Rank112271110.22124/jart.2017.2711ENP.Manuel Dominguez WadeDepartment of
Mathematics, Matanzas University, Matanzas, CubaJournal Article20170610Let $k$ be field of characteristic $p$, and<br />let $G$ be any finite group with splitting field $k$. Assume that $B$ is a $p$-block of $G$.<br />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 permutation<br />module 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.https://jart.guilan.ac.ir/article_2711_8f0e0342d1bad2b4ab66eb7767948d0e.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315220171201On subalgebras of an evolution algebra of a "chicken" population1324271210.22124/jart.2017.2712ENU.A.RozikovInstitute of Mathematics, Tashkent, UzbekistanB.A.OmirovInstitute of Mathematics, Tashkent. UzbekistanJournal Article20170919We consider an evolution algebra which corresponds to a<br /> bisexual population with a set of<br /> females partitioned into finitely many different types<br /> and the males having only one type. For such algebras in<br /> terms of its structure constants we calculate right and plenary<br /> periods of generator elements. Some results on subalgebras of EACP<br /> and ideals on low-dimensional EACP are obtained.https://jart.guilan.ac.ir/article_2712_222c9e56b9aa274159d6c55d5619763d.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315220171201Algebraic adjoint of the polynomials-polynomial matrix multiplication2533271310.22124/jart.2017.2713ENR.AndriamifidisoaDepartment of Mathematics and Computer Science, University of Antananarivo, Antananarivo, MadagascarH.RandriambolasataDepartment of
Mathematics and Computer Science, University
of Antananarivo, Antananarivo, MadagascarJournal Article20171114This 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 fieldhttps://jart.guilan.ac.ir/article_2713_513fa552e02ac910322e1193e698e82b.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315220171201σ-sporadic prime ideals and superficial elements3545271410.22124/jart.2017.2714END.KamanoD\'epartment de Sciences et Technologie, Section Math\'ematiques, Ecole normale sup\'erieure, Abidjan, C\^ote d'IvoireK.A.EssanUFR sciences sociales, Universit'e P'el'eforo Gon Coulibaly, Korhogo, C^ote d'IvoireA.AbdoulayeLaboratoire de
Math\'ematiques et Informatique, Universit\'e Nangui Abrogoua, Abidjan, C\^ote d'IvoireE.D.AkekeUFR de Math'ematiques et Informatique, Universit'e F'elix Houphouet Boigny, Abidjan, C^ote d'IvoireJournal Article20171203Let $A$ 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<br /> $S^{\sigma}_{n}(I)=Ass(A/\sigma(I^n))\setminus A_{\sigma}(I)$, with $n$ small, which are the sets of $\sigma$-sporadic prime divisors of $I$.<br />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 $f_I=(I^n)_{n\in\mathbb{N}}$.https://jart.guilan.ac.ir/article_2714_3bb28c732e69e2ea353a223c92597da3.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315220171201On the additive maps satisfying Skew-Engel conditions4758271510.22124/jart.2017.2715ENM.NadeemDepartment of
Mathematics, Government College University, Lahore, PakistanM.AslamDepartment of
Mathematics, Government College University, Lahore, PakistanY.AhmedDepartment of
Mathematics, Government College University, Lahore, PakistanJournal Article20170929Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:I\rightarrow R$ be an additive<br />map. Then skew-Engel condition $\langle... \langle \langle$<br />$f(x),x^{n_1} \rangle,x^{n_2} \rangle ,...,x^{n_k} \rangle=0$ 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.<br /> This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.https://jart.guilan.ac.ir/article_2715_db25ae4c151c5a154173eaca9ba7e7fa.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315220171201Self-cogenerator modules and their applications5968271610.22124/jart.2017.2716ENY.TalebiDepartment of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, IranM.HosseinpourDepartment of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, IranJournal Article20171210Let $R$ be a ring and $M$ be a right $R$-module. In this paper, we give some properties of self-cogenerator<br />modules. If $M$ is self-cogenerator and $S = End_{R}(M)$ is a cononsingular ring, then $M$ is a<br />$\mathcal{K}$-module. It is shown that every self-cogenerator Baer is dual Baer.https://jart.guilan.ac.ir/article_2716_e72e91aabb355c0e3f819156779a3c44.pdf