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Algebraically Independent
Definition
Let K be a field, and A a K-algebra. Elements y_1, ..., y_n are algebraically independent over K if the natural surjection K[Y_1, ..., Y_n]->K[y_1, ..., y_n] is an isomorphism. In other words, there are no polynomial relations F(y_1, ..., y_n) = 0 with coefficients in K.