Student Commutative Algebra Seminar

The Buchsbaum-Eisenbud exactness theorem establishes a useful criterion for the exactness of a sequence of free modules over a Noetherian ring. In this talk, I will first demonstrate a criterion of McCoy on injectivity of maps between free modules. I will then deduce the Buchsbaum-Eisenbud exactness theorem as a natural extension of this result of McCoy. Time abiding, I will explain some uses and extensions of the theorem. I will assume some familiarity with localizations and linear algebraic tools.
Speaker(s): Calvin Yost-Wolff (UM)