Reconstructing projective modules from its trace ideal

We make a detailed study of idempotent ideals that are traces of countably generated projective right modules. We associate to such ideals an ascending chain of finitely generated left ideals and, dually, a descending chain of cofinitely generated right ideals. The study of the first sequence allows us to characterize trace ideals of projective modules and to show that projective modules can always be lifted modulo the trace ideal of a projective module. As a consequence we give some new classification results of (countably generated) projective modules over particular classes of semilocal rings. The study of the second sequence leads us to consider projective modules over noetherian FCR-algebras; we make some constructions of non-trivial projective modules showing that over such rings the behavior of countably generated projective modules that are not direct sum of finitely generated ones is, in general, quite complex.Comment: 29 page

Pure projective torsion free modules over Bass domains

We prove that every pure projective torsion free module over a (commutative) Bass domainwith finite normalization contains a finitely generated direct summand

Experimental and Numerical Modelling of Turbulent Flow over an Inclined Backward-Facing Step in an Open Channel

The contribution deals with the experimental and numerical modelling of the turbulent flow over an inclined backward-facing step in an open water channel. The modelling was carried out in the wide range of the Froude number covering the subcritical, supercritical and near critical regimes as well. The study was concentrated particularly on the development of flow separation and on changes of free surface. Numerical results obtained using the commercial software ANSYS CFX 12.0 for the two-equation SST model and the EARSM model were compared with experimental data obtained by means of PIV and LDA measuring techniques

Projective modules over the Gerasimov-Sakhaev counterexample

We 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