# About maximal Cohen-Macaulay modules

I´m trying to solve a problem of cancellation of reflexive finitely generated modules over normal noetherian domains. When $R$ is regular domain with $\dim R \le 2$, for finitely generated modules, reflexive is equivalent to projective.

Now I´m studying the case $\dim R=2$ and $R$ normal. In this hypothesis, reflexive modules are maximal Cohen-Macaulay modules.

I´m looking for references about this topic, with especial emphasis in lifting of homomorphism between factors of maximal CM modules: something like "... an homomorphism $M/IM\to N/IN$ can be lift to an homomorphism $M\to N...$"; indescomponibles maximal CM modules are welcome too.

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