Browsing by Author "Labra, Alicia"

Now showing items 1-14 of 14

    • An equivalence in generalized almost-Jordan algebras 
      Guzzo, Henrique; Labra, Alicia (Universidad Catolica del Norte, 2016)
      In this paper we work with the variety of commutative algebras satisfying the identity β((x2y)x - ((yx)x)x)+γ(x3y - ((yx)x)x) = 0, where β, γ are scalars. They are called generalized almost-Jordan algebras. We prove that ...
    • Automorphisms in a class of Jordan Bernstein algebras of order 2 
      Labra, Alicia (Marcel Dekker Inc., 1997)
    • Generalized Jordan algebras 
      Hentzel, Irvin Roy; Labra, Alicia (2007)
      We study commutative algebras which are generalizations of Jordan algebras. The associator is defined as usual by (x, y, z) = (x y)z - x(y z). The Jordan identity is (x2, y, x) = 0. In the three generalizations given below, ...
    • Nilpotency of commutative finitely generated algebras satisfying Lx3+γLx3=0, γ=1,0 
      Correa, Ivan; Hentzel, Irvin Roy; Labra, Alicia (2011)
      This paper deals with two varieties of commutative non-associative algebras. One variety satisfies Lx3+Lx3=0. The other variety satisfies Lx3=0. We prove that in either variety, any finitely generated algebra is nilpotent. ...
    • On left nilalgebras of left nilindex four satisfying an identity of degree four 
      Hentzel, Irvin Roy; Labra, Alicia (2007)
      We extend the concept of commutative nilalgebras to commutative algebras which are not power associative. We shall study commutative algebras A over fields of characteristic ≠ 2, 3 which satisfy the identities x(x(xx)) = ...
    • On nilpotency of generalized almost-jordan right-nilalgebras 
      Arenas, Manuel; Labra, Alicia (World Scientific Publishing Co. Pte Ltd, 2008)
      We study the variety of algebras A over a field of characteristic ≠ 2, 3, 5 satisfying the identities xy=yx and β ((xx)y)x-((yx)x)x + γ ((xx)x)y-((yx)x)x=0, where β, γ are scalars. We do not assume power-associativity. We ...
    • On plenary train algebras of rank 4 
      Labra, Alicia; Suazo, Avelino (2007)
      The existence of idempotent elements in plenary train algebras of rank greater than 3, is an open problem to be solved. J. Carlos Gutierrez's results on plenary train algebras in Gutierrez (2000) are based on the underlying ...
    • On representations on right nilalgebras of right nilindex four 
      Hentzel, Irvin Roy; Labra, Alicia (2005)
      We shall study representations of algebras over fields of characteristic ≠ 2, 3 of dimension 4 which satisfy the identities xy - yx = 0, and ((xx)x)x = 0. In these algebras the multiplication operator was shown to be ...
    • On some Jordan baric algebras 
      Elduque, Alberto; Labra, Alicia (2013)
      Several classes of baric algebras studied by different authors will be given a unified treatment, using the technique of gametization. Most of these algebras will be shown, using straightforward arguments, to be either ...
    • On the classification of commutative right-nilalgebras of dimension at most four 
      Elduque, Alberto; Labra, Alicia (2007)
      Gerstenhaber and Myung (1975) classified all commutative, power-associative nilalgebras of dimension 4. In this article we extend Gerstenhaber and Myung's results by giving a classification of commutative right-nilalgebras ...
    • On the nilpotence of the multiplication operator in commutative right nil algebras 
      Correa, Ivan; Hentzel, Irvin Roy; Labra, Alicia (2002)
      We study conditions under which the identity ((xx)x)x = 0 in a commutative nonassociative algebra A implies Rx is nil-potent where Rx is the multiplication operator Rx(y) = xy for all y in A. The separate conditions that ...
    • Representations of Generalized Almost-Jordan Algebras 
      Flores, Marcelo; Labra, Alicia (Taylor and Francis Inc., 2015)
      © 2015, Copyright Taylor & Francis Group, LLC. This paper deals with the variety of commutative algebras satisfying the identity β{(yx <sup>2</sup>)x − ((yx)x)x} + γ{yx <sup>3</sup> − ((yx)x)x} = ...
    • Representations on train algebras of rank 3 
      Labra, Alicia; Reyes, Cristián (2005)
      We give a characterization of the representations on train algebras of rank 3. We prove that the subalgebra of the algebra of endomorphisms of a module generated by the representation of the nil ideal of the algebra is ...
    • Solvability of commutative right-nilalgebras satisfying (b(aa))a = b((aa)a) 
      Correa, Iván; Hentzel, Irvin Roy; Labra, Alicia (Universidad Catolica del Norte, 2010)
      We study commutative right-nilalgebras of right-nilindex four satisfying the identity (b(aa))a = b((aa)a). Ourmainresultisthatthese algebras are solvable and not necessarily nilpotent. Our results require characteristic 6≠2, 3, 5.