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Title: Pure-injective modules over tubular algebras and string algebras
Author: Harland, Richard James
ISNI:       0000 0004 2702 8716
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2011
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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.
Supervisor: Prest, Michael ; Puninskiy, Gennady Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: String Algebras ; Tubular Algebras ; Lattice Dimension ; Pure-Injective Modules ; Superdecomposable modules ; slope ; Wide lattices ; Infinite dimensional string modules