Gennadi Puninski

Some Model Theory Over an Exceptional Uniserial Ring and Decompositions of Serial Modules

An example is given of a direct summand of a serial module that does not admit an indecomposable decomposition.

Superdecomposable pure-injective modules exist over some string algebras

We prove that over every non-domestic string algebra over a countable field there exists a superdecomposable pure-injective module.

Superdecomposable pure-injective modules and integral group rings

We prove that if G is a non-trivial finite group, then the integral group ring

∑–pure—injective modules over a commutative prüfer ring

\mathbb{Z} G

Rings described by various purities

possesses a superdecomposable pure-injective module.

When every finitely generated flat module is projective

We give the complete classification of ∑-pure-injective modules over a commutative Prufer ring.