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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:532205 |
| Date | January 2011 |
| Creators | Harland, Richard James |
| Contributors | Prest, Michael ; Puninskiy, Gennady |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/pureinjective-modules-over-tubular-algebras-and-string-algebras(5cc94d54-4f76-4801-8bdc-1588f543d32e).html |
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