UTA Department of Mathematics

Algebra Seminar

Date/Time/Room: Friday (9/28/2007) at 4:00pm in 438 Pickard Hall

Speaker: Meri Hughes
Department of Mathematics
The University of Texas at Arlington

"On infinite syzygies"

Abstract: A module $M$ is an {\it infinite syzygy module} if it is isomorphic to the image of a differential in a minimal acyclic complex of free $R$-modules. This talk explores some unanswered questions regarding this phenomena. Given a minimal acyclic complex of free modules, under what conditions does {\it branching} occur, i.e., does there exist a second complex that is isomorphic to the first to the left of an initial point, but not isomorphic to the right? We also investigate the circumstances for which we can extend the free resolution of a module to the right, through a process of dualization. Conditions and examples supplying partial answers to these questions will be presented.