Ivan Correa

On the solvability of the commutative power-associative nilalgebras of dimension 6

Abstract We prove that commutative power-associative nilalgebras of dimension 6 over a field of characteristic ≠2,3,5 are solvable.

On the Solvability of the Five Dimensional Commutative Power-Associative Nilalgebras

We prove that commutative power-associative nilalgebras of dimension 5 are solvable.

ON THE NILPOTENCE OF THE MULTIPLICATION OPERATOR IN COMMUTATIVE RIGHT NIL ALGEBRAS

ABSTRACT We study conditions under which the identity in a commutative nonassociative algebra A implies is nilpotent where is the multiplication operator for all in A. The separate conditions that we found to be sufficient are (1) dimension four or less, (2) any additional non-trivial identity of degree four, or (3) We assume characteristic

Shape identities in bernstein algebras

We study the shape identities arising in the theory of Bernstein algebras. We determine all shape identities of minimal degree for two subclasses of Bernstein algebras, namely, normal Bernstein algebras and exceptional Bernstein algebras.

On Flexible Algebras Satisfying x(yz) = y(zx)

In this paper we study flexible algebras (possibly infinite-dimensional) satisfying the polynomial identity x(yz) = y(zx). We prove that in these algebras, products of five elements are associative and commutative. As a consequence of this, we get that when such an algebra is a nil-algebra of bounded nil-index, it is nilpotent. Furthermore, we obtain optimal bounds for the index of nilpotency. Another consequence that we get is that these algebras are associative when they are semiprime.

A NOTE ON QUASI n-MAPS

Using a factorization of quasi n-maps we find a relationship between the module formed by the n-maps and the module formed by the quasi n-maps. In particular, we characterize the quasi cubic forms using a relation called the parallelepiped law. Moreover we give necessary and sufficient conditions for the equality of the modules of quasi cubic forms and cubic forms for any module M.