Defined differential

If the base ring k is not plain from context, we write explicitly 2 /t. Clearly we can also construct 2 for 4 not finitely generated just by extending the preliminary computation to polynomial rings in infinitely many variables. When S is a closed set in k", the elements of 2 s] are the (algebraic) differentials defined on S—combinations of the dxt multiplied by functions. In general therefore we call 2 the module of differentials of 4. 

The components of SCRM may again be differentially defined in terms of the subdivision of the particular strands, although most definitions would eneompass the following ... 

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