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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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Remarks on primitivity of polynomial rings
by
Agata Smoktunowicz
Yale University, New Haven

It is known that the polynomial ring R[x] over non primitive ring R can be primitive (examples:Hodges 1984, Bergman 1995). We study two connected questions:

If R is a nil ring is R[x] not primitive?

If R is Jacobson radical is R[x] not primitive?

Recall that the statement: R[x] is not semiprimitive for all nil rings R is equivalent, as proved by Krempa, to the Kothe's Conjecture (1930) ''If a ring R has no two sided nil ideals then R has no one sided nil ideals''.

Date received: February 17, 2002

Copyright © 2002 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 # caig-77.