There will be one meeting in Atlanta and one meeting in Columbia each semester. For information about the Atlanta meeting please see web page for Atlanta meeting.
Title: Direct sums of DG-injective complexes
Abstract:
For a given ring $R$ we show that every direct sum of
DG-injective complexes of $R$-modules is still DG-injective if and only
if
$R$ is noetherian and every complex of injective $R$-modules is a
DG-injective complex. We use this result to prove that over a
commutative
noetherian ring of finite Krull dimension the class of DG-injective
complexes is closed under direct sums if and only if the ring has
finite
global dimension. We also show that if $R$ is a commutative noetherian
ring of finite Krull dimension such that $id M = \#-id M$ for any
complex
$M$, then $R$ has finite global dimension.
2- 2:50 pm Florian Enescu, Georgia State University
Title: Frobenius depth
Abstract: We will discuss a class of prime ideals, called F-stable
primes,
for rings of characteristic p, p prime. We will relate them to notion
of
Frobenius depth of a local ring as introduced and studied by Gennady
Lyubeznik in his recent work, and, subsequently, work of A. K. Singh
and
U. Walther.
3:05 -3:55 pm Yongwei Yao, Georgia State University
Title:Test exponents for Artinian modules
Abstract: We prove the existence of a test exponent for any given
Artinian
R-module. Applying this result to the highest local cohomology module,
we
give an alternate proof of the existence of a test exponent for all
ideals
generated by (full or partial) systems of parameters (due to R. Y.
Sharp).
Time permitting, I will talk about how this is applied to modules of
finite projective dimension and how this allows us to define a somewhat
`new' F-rational signature. This is joint work with Mel Hochster.
$:10 -5 pm Hamid Rahmati, University of Nebraska, Lincoln
Title: Contracting Endomorphisms and Gorenstein Modules