The behaviour of the Hasse-Schmidt algebra of higher derivations under localization is studied using Andr\'e cohomology. Elementary techniques are used to describe the Hasse-Schmidt derivations on certain monomial rings in the nonmodular case. The localization conjecture is then verified for all monomial rings.

MSC Classifications:

13D03, 13N10 show english descriptions (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen, cyclic, dihedral, etc.)
Rings of differential operators and their modules [See also 16S32, 32C38] 13D03 - (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen, cyclic, dihedral, etc.)
13N10 - Rings of differential operators and their modules [See also 16S32, 32C38]

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