  We first present a Skoda type division theorem for holomorphic sections of
line bundles on a projective variety which is essentially the most general,
compared to previous ones. It is derived from Varolin's theorem as a corollary.
Then we revisit Geometric Effective Nullstellensatz and observe that even this
general Skoda division is far from sufficient to yield stronger Geometric
Effective Nullstellensatz such as `vanishing order $1$ division', which could
be used for finite generation of section rings by the basic finite generation
lemma. To resolve this problem, we develop a notion of pseudo-division and show
that it can replace the usual division in the finite generation lemma. We also
give a vanishing order 1 pseudo-division result when the line bundle is ample.

Algebraic Geometry;Complex Variables