Fouche, W.L.2013-09-072005-07-262013-09-072003-04-012006-07-262005-07-22De Wet, PO 2002, The division theorem for smooth functions, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/26530 >H735/aghttp://hdl.handle.net/2263/26530Dissertation (MSc (Mathematics))--University of Pretoria, 2006.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.Differential equations partialAnalytic functionsCommutative algebraSmoothness of functionsUCTDDissertationhttp://upetd.up.ac.za/thesis/available/etd-07222005-122154/