We show that, for any tubular algebra, the lattice of ppdefinable subgroups of the direct sum of all indecomposable pureinjective modules of slope r has mdimension 2 if r is rational, and undefined breadth if r is irrational and hence that there are no superdecomposable pureinjectives of rational slope, but there are superdecomposable pureinjectives of irrational slope, if the underlying field is countable.We determine the pureinjective hull of every direct sum string module over a string algebra. If A is a domestic string algebra such that the width of the lattice of ppformulas has defined breadth, then classify "almost all" of the pureinjective indecomposable Amodules.
Date of Award  1 Aug 2011 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Michael Prest (Supervisor) & Gennady Puninskiy (Supervisor) 

 slope
 Infinite dimensional string modules
 Wide lattices
 Superdecomposable modules
 Tubular Algebras
 Lattice Dimension
 String Algebras
 PureInjective Modules
PureInjective Modules over Tubular Algebras and String Algebras
Harland, R. (Author). 1 Aug 2011
Student thesis: Phd