Document Type	Master's Dissertation
Author	De Wet, Pieter Oloff
URN	etd-07222005-122154
Document Title	The division theorem for smooth functions
Degree	MSc (Mathematics)
Department	Mathematics and Applied Mathematics
Supervisor	Advisor Name Title Prof W L Fouche Committee Chair
Keywords	differential equations partial analytic functions commutative algebra smoothness of functions
Date	2003-04-01
Availability	unrestricted
Abstract We discuss Lojasiewicz's beautiful proof of the division theorem for smooth functions. The standard proofs are based on the Weierstrass preparation theorem for analytic functions and use techniques from the theory of partial differential equations. Lojasiewicz's approach is more geometric and syn¬thetic. In the appendices appear new proofs of results which are required for the theorem. © 2002, 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. Please cite as follows: De Wet, PO 2002, The division theorem for smooth functions, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-07222005-122154/ > H735/ag
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