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The ring of * microdifferential operators* with constant
coefficients

is a discrete valuation ring and
is a free
-module
of rank . For ,
is bijective and hence
is a
-automorphism of
mapping the trivial
-structure to that of
.
Hence,
is a free
-module of
rank
.
In particular, , resp.
, is a free
-module of rank for , resp.
. Hence,
is a -dimensional
vector space over the quotient field
. Since
and
,
is a free
-module of rank .

*Christoph Lossen*

*2001-03-21*