LEMMA 04.1Let
be a commutative ring. Then for the polynomial ring
of
-variables over
, the module
of
-differentials of
over
is equal to a free module
generated by
. Namely, we have

LEMMA 04.2Let
be a ring. Let
be
-algebras. Then for any
-algebra
homomorphism
we have

LEMMA 04.3Let
be a commutative ring.
Let
be a commutative
-algebra. Then for any ideal
of
, we have
the following exact sequence: