Abstract:
Let A ! A0 be a regular morphism of Noetherian rings,any A-morphism v :
B ! A0 with B an A-algebra of finite type,factors through a smooth A-algebra C,
that is v is a composite A-morphism B ! C ! A0. The A-algebra C is called a
General Neron Desingularization.
In this thesis we give a uniform General Neron Desingularization for one dimen-
sional local rings with respect to morphisms which coincide modulo a high power
of themaximalideal.TheresulthasinterestingapplicationsinthecaseofCohen-
Macaulay rings.
Moreover, as our another contribution,we give an easy proof of the General
Neron Desingularization in the frame of regular morphisms between Artinianlocal
rings and Noetherian local rings of dimension one. We also give algorithms to
construct theN´eron Desingularization in different cases.
