Pi-complemented algebras
For an ideal U of a nonassociative algebra A, the
pi-closure of U is defined by overline{U} = Ann(Ann(U)),
where Ann(.) denotes the annihilator relative
to the algebra A. An algebra A is said to be
pi-complemented if for every pi-closed ideal U of A
there exists a pi-closed ideal V of A such that A is the
direct sum of U and V. In this paper we shall develop
a structure theory for pi-complemented algebras.
(This paper has appeared under the title "Pi-complemented algebras through
pseudocomplemented lattices" in Order 29 (2012), 463--479)
J. C. Cabello < jcabello@ugr.es >
M. Cabrera < cabrera@ugr.es >