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

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