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math.AC2009
The depth formula for modules with reducible complexity
Petter Andreas Bergh, David Jorgensen
We prove that the depth formula holds for $\Tor$-independent modules in certain cases over a Cohen-Macaulay local ring, provided one of the modules has reducible complexity.
math.AC2004
Independence of the total reflexivity conditions for modules
David Jorgensen, Liana Sega
We show that the conditions defining total reflexivity for modules are independent. In particular, we construct a commutative Noetherian local ring and a reflexive -module $…
math.AC2003
Nonvanishing cohomology and classes of Gorenstein rings
David A. Jorgensen, Liana M. Sega
We give counterexamples to the following conjecture of Auslander: given a finitely generated module over an Artin algebra , there exists a positive integer such that f…