UTA Department of Mathematics

Algebra Seminar

Date/Time/Room: Friday (10/22/2004) at 4:00pm in 487 Pickard Hall

Speaker: A.J. Todd, Department of Mathematics, University of Texas at Arlington

"Finite Free Resolutions Generated by Three Elements"

Abstract: In 1974, Buchsbaum and Eisenbud published a paper in Advances in Mathematics, in which they conjectured that "...'every' finite free resolution is the free resolution of a 3-generated ideal." Bruns, 1976, published a paper in Journal of Algebra which proves this conjecture. This talk will give the necessary basics for the proof of the conjecture, including defining and proving the existence of basic elements and the reduction of the rank of an m-torsionless module. We will then prove the conjecture itself. A moderate amount of commutative ring and module theory will be assumed. Finally, if time allows, I will give an introduction to research based on the paper that I am currently working on under the supervision of Dr. David Jorgensen.