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`http://hdl.handle.net/2381/30527`

Title: | Finiteness conditions on the Ext-algebra |

Authors: | Davis, Gabriel. |

Award date: | 2005 |

Presented at: | University of Leicester |

Abstract: | Let A be a finite-dimensional algebra given by quiver and monomial relations. In [18] we see that the Ext-algebra of A is finitely generated only if all the Ext-algebras of certain cycle algebras overlying A are finitely generated. Here a cycle algebra Lambda is a finite-dimensional algebra given by quiver and monomial relations where the quiver is an oriented cycle. The main result of this thesis gives necessary and sufficient conditions for the Ext-algebra of such a Lambda to be finitely generated; this is achieved by defining a computable invariant of Lambda, the smo-tube. We also give necessary and sufficient conditions for the Ext-algebra of Lambda to be Noetherian.;Let Lambda be a triangular matrix algebra, defined by algebras T and U and a T-U-bimodule M. Under certain conditions we show that if the Ext-algebras of T and U are right (respectively left) Noetherian rings, then the Ext-algebra of Lambda is a right (respectively left) Noetherian ring. An example shows the hypotheses used cannot be improved. We also specialise to the case where Lambda is a one-point extension: we give a specific presentation of a result that parallels a similar theorem for the more general case above. |

Links: | http://hdl.handle.net/2381/30527 |

Type: | Thesis |

Level: | Doctoral |

Qualification: | PhD |

Rights: | Copyright © the author. All rights reserved. |

Appears in Collections: | Theses, Dept. of Mathematics Leicester Theses |

Files in This Item:

File | Description | Size | Format | |
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U190511.pdf | 2.94 MB | Adobe PDF | View/Open |

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