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Algebra and Related Topics - Volume:5 Issue: 2, Autumn 2017

Journal of Algebra and Related Topics
Volume:5 Issue: 2, Autumn 2017

  • تاریخ انتشار: 1396/10/30
  • تعداد عناوین: 6
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  • P. Manuel Dominguez Wade * Pages 1-12
    Let k be field of characteristic p , and let 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 permutation 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.
    Keywords: Radical vertex, G -weight, p -local rank
  • U.A. Rozikov, B.A. Omirov * Pages 13-24
    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.
    Keywords: Evolution algebra, bisexual population, associative algebra, subalgebra
  • R. Andriamifidisoa *, H. Randriambolasata Pages 25-33
    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.
    Keywords: Operator in the shifts, scalar product, algebraic adjoint
  • D. Kamano *, K.A. Essan, A. Abdoulaye, E.D. Akeke Pages 35-45
    Let A be a Noetherian ring, I be an ideal of A and σ 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 σ(I n ) , which denoted by Ass(A/σ(I n )) , stabilize to A σ (I) . We give some properties of the setsS σ n (I)=Ass(A/σ(I n ))∖A σ (I) , with n small, which are the sets of σ -sporadic prime divisors of I .
    We also give some relationships between σ(f I ) -superficial elements and asymptotic prime σ -divisors, where σ(f I ) is the σ -closure of the I -adic filtration f I =(I n ) n∈N.
    Keywords: Noetherian ring, Filtration, semi-prime operation, associated prime ideals, superficial elements
  • M. Nadeem *, M. Aslam, Y. Ahmed Pages 47-58
    Let R be a prime ring, I be any nonzero ideal of R and f:I→R be an additive map. Then skew-Engel condition ⟨...⟨⟨f(x),xn1⟩,xn2⟩,...,xnk⟩=0 implies that f(x)=0 ∀x∈I provided 2≠ char (R)>n1齯..., where n1,n2,...,nk are natural numbers. This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.
    Keywords: Additive map, prime ring, semiprime ring, MA-semiring
  • Y. Talebi, M. Hosseinpour * Pages 59-68
    Let R be a ring and M be a right R-module. In this paper, we give some properties of self-cogenerator modules. If M is self-cogenerator and S=EndR(M) is a cononsingular ring, then M is a K -module. It is shown that every self-cogenerator Baer is dual Baer.
    Keywords: Self-cogenerator modules, Baer rings, modules, dual Baer modules