Pure-Injective Modules over Tubular Algebras and String Algebras

  • Richard Harland

Student thesis: Phd


We show that, for any tubular algebra, the lattice of pp-definable subgroups of the direct sum of all indecomposable pure-injective modules of slope r has m-dimension 2 if r is rational, and undefined breadth if r is irrational- and hence that there are no superdecomposable pure-injectives of rational slope, but there are superdecomposable pure-injectives of irrational slope, if the underlying field is countable.We determine the pure-injective 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 pp-formulas has defined breadth, then classify "almost all" of the pure-injective indecomposable A-modules.
Date of Award1 Aug 2011
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorMichael Prest (Supervisor) & Gennady Puninskiy (Supervisor)


  • slope
  • Infinite dimensional string modules
  • Wide lattices
  • Superdecomposable modules
  • Tubular Algebras
  • Lattice Dimension
  • String Algebras
  • Pure-Injective Modules

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