Commutative Algebra and its Interactions A conference in honor of Mel Hochster July 31 - August 5, 2008 Abstract Detail   Title: Embedding theorems and uniform test exponents Assume R is a commutative Noetherian ring and all modules are finitely generated. Then the embedding theorem states that every R-module of finite projective dimension embeds into a finite direct sum of cyclic R-modules each of which is the quotient of R by an ideal generated by an R-regular sequence. In fact, this embedding theorem applies to all R-modules of finite G-dimension. Further assume R is a domain of prime characteristic. Then, under mild conditions (e.g., R is essentially of finite type over a complete local ring or an F-finite homomorphic image of a Gorenstein ring), there exists a (fixed) module-finite extension domain S of R with the following property: For every R-module of finitely phantom projective dimension, its scalar extension to S WEAKLY embeds into a finite direct sum of cyclic S-modules each of which is the quotient of S by a parameter ideal. Here a weak embedding means a linear map whose kernel is contained in the tight closure of 0. As an application of the above weak embedding theorem, we can show the existence of (uniform) test exponents for all modules of finite phantom projective dimension. All the above results are joint work with Mel Hochster. Time permitting, I will also talk about the existence of (uniform) test exponents for all R-modules if R has finite F-representation type. Yongwei Yao Georgia State University Email:  yyao@gsu.edu Phone: (770) 234-4912   BACK to Speaker Listing BACK to Conference Home