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Message Subject @@@This is YOUR lucky day; I am a great intellect and there is no question I cannot answer. --shoot and be amazed !
Poster Handle AlphaWolf
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R- to S be a local homomorphism of complete local domains. Then there exists an R-algebra BR that is a balanced big Cohen–Macaulay algebra for R, an S-algebra {\displaystyle B_{S}}{\displaystyle B_{S}} that is a balanced big Cohen-Macaulay algebra for S, and a homomorphism BR - BS such that the natural square given by these maps commutes.
 
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