I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 1, PAGES 127-141
Almost primitive elements of free nonassociative algebras of small
A. V. Klimakov
A. A. Mikhalev
View as HTML
View as gif image
a field, , and let be the free
nonassociative algebra over the field with the
A. G. Kurosh proved that subalgebras of free nonassociative
algebras are free.
A subset of nonzero elements of
the algebra is said to be
primitive if there is a set of free generators of
that (in this case we
A nonzero element of the free algebra
is said to
be an almost primitive if is not a primitive
element of the algebra , but is a primitive
element of any proper subalgebra of that contains it.
In this article, for free nonassociative algebras of rank and criteria for homogeneous
elements to be almost primitive are obtained and algorithms to
recognize homogeneous almost primitive elements are constructed.
New examples of almost primitive elements of free nonassociative
algebras of rank are constructed.
Last modified: January 31, 2012