Ring Properties Described in the Language of Torsion Preradicals
by
John Eric van den Berg
University of Natal, Pietermaritzburg, South Africa

If R is an arbitrary ring with identity then the set torsp R of all torsion preradicals on Mod-R has the structure of a lattice ordered left residuated integral monoid. It is shown that several primeness and semiprimeness conditions (including right strongly prime and right strongly semiprime) can be characterized in terms of properties of torsp R. These properties are, for the most part, first order sentences in the language of torsp R. It is also shown that certain classes of QF rings lend themselves to a similar characterization.

Date received: January 7, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-47.