Strongly prime pseudomultiplicative lattices.
by
Maria Isabel Tocon Barroso
University of Malaga

If we define prime element in a pseudomultiplicative lattice L in a natural way, it is straightforward to see that if the meet of the set of the prime elements is 0, then L is semiprime. Since an associative ring is semiprime if, and only if, the intersection of its prime ideals is 0, the converse is true for the lattice of ideals of a semiprime ring. However, as we will show in this talk, this does not remain true in general. Also we will obtain positive answers for particular cases. The content of this talk is part of "Pseudocomplemented semilattices, Boolean algebras and compatible products" (Journal of Algebra, 242, 60-91, 2001) jointly written with Prof. Fernandez Lopez.

Date received: February 3, 2003