45 research outputs found
Ringel's conjecture for domestic string algebras
We classify indecomposable pure injective modules over domestic string
algebras, verifying Ringel's conjecture on the structure of such modules.Comment: minor correction
Projective modules over the endomorphism ring of a biuniform module
AbstractWe investigate infinitely generated projective modules over the endomorphism ring of a biuniform module
The generating hypothesis in the derived category of a ring
We show that a strong form (the fully faithful version) of the generating
hypothesis, introduced by Freyd in algebraic topology, holds in the derived
category of a ring R if and only if R is von Neumann regular. This extends
results of the second author. We also characterize rings for which the original
form (the faithful version) of the generating hypothesis holds in the derived
category of R. These must be close to von Neumann regular in a precise sense,
and, given any of a number of finiteness hypotheses, must be von Neumann
regular. However, we construct an example of such a ring that is not von
Neumann regular, and therefore does not satisfy the strong form of the
generating hypothesis
Decidability of the theory of modules over Pr\"ufer domains with infinite residue fields
We provide algebraic conditions ensuring the decidability of the theory of
modules over effectively given Pr\"ufer (in particular B\'ezout) domains with
infinite residue fields in terms of a suitable generalization of the prime
radical relation. For B\'{e}zout domains these conditions are also necessary.Comment: Updated so that the title and abstract matches the published version.
Other minor corrections and changes mad
Krull-Gabriel dimension and the model-theoretic complexity of the category of modules over group rings of finite groups
Projective modules over the Gerasimov–Sakhaev counterexample
AbstractWe investigate the structure of the so-called Gerasimov–Sakhaev counterexample, which is a particular example of a universal localization, and classify (both finitely and infinitely generated) projective modules over it