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On Clifford A-algebras and a framework for localization of A-modules
Thesis (PhD)--University of Pretoria, 2015.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2015
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| _version_ | 1867613679918252032 |
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| access_status_str | Open Access |
| author2 | Ntumba, Patrice P. |
| author_browse | Ntumba, Patrice P. |
| author_facet | Ntumba, Patrice P. |
| collection | Thesis |
| dc_rights_str_mv | © 2015 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD)--University of Pretoria, 2015. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/45954 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:59.298Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/45954 On Clifford A-algebras and a framework for localization of A-modules Ntumba, Patrice P. Yizengaw, Belayneh Yibeltal UCTD Thesis (PhD)--University of Pretoria, 2015. Nowadays, Clifford A-algebras are hot areas of research due to their applicability to di erent disci- plines; capacity to create relationship between quadratic and linear A-morphisms; and relation to tensor A-algebras. In this work, we investigate the commutative property of the Cli ord functor on sheaves of Cli ord algebras, the natural ltration of Cli ord A-algebras, and localization of vector sheaves; out of which two papers are extracted for publication [43], [44]. To present the thesis in a coherent way, we organize the thesis in ve chapters. Chapter 1 is a part where relevant classical results are reviewed. Chapter 2 covers basic results on Cli ord A-algebras of quadratic A-modules (which are of course results obtained by Prof. PP Ntumba [42]). In Chapter 3, we discuss the commutativity of the Cli ord functor Cl and the algebra extension functor (through the tensor product) of the ground algebra sheaf A of a quadratic A-module (E; q). We also observe the existence of an isomorphism between the functors S1 and (S1A) {. As a particular case, we show the commutativity of the Cli ord functor Cl and the localization functor S1. A discussion about the localization of A-modules at prime ideal subsheaves and at subsheaves induced by maximal ideals is also included. In Chapter 4, we study two main A-isomorphisms of Cli ord A-algebras: the main involution and the anti-involution A-isomorphisms, which split Cli ord A-algebras into even sub-A-algebras and sub-A-modules of odd products. Next, we give a de nition for the natural ltration of Cli ord A- algebras and show that for every A-algebra sheaf E, endowed with a regular ltration, one obtains a new graded A-algebra sheaf, denoted Gr(E), which turns out to be A-isomorphic to E. A conclusive remark and list of research topics that can be addressed in connection with this research do appear in Chapter 5. tm2015 Mathematics and Applied Mathematics PhD Unrestricted 2015-07-02T11:06:09Z 2015-07-02T11:06:09Z 2015/04/16 2015 Thesis Yizengaw, BY 2015, On Clifford A-algebras and a framework for localization of A-modules, PhD Thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/45954> A2015 http://hdl.handle.net/2263/45954 en © 2015 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD On Clifford A-algebras and a framework for localization of A-modules |
| title | On Clifford A-algebras and a framework for localization of A-modules |
| title_full | On Clifford A-algebras and a framework for localization of A-modules |
| title_fullStr | On Clifford A-algebras and a framework for localization of A-modules |
| title_full_unstemmed | On Clifford A-algebras and a framework for localization of A-modules |
| title_short | On Clifford A-algebras and a framework for localization of A-modules |
| title_sort | on clifford a algebras and a framework for localization of a modules |
| topic | UCTD |
| url | http://hdl.handle.net/2263/45954 |