algebraically independent

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algebraically independent [¦al·jə¦brā·ik·lē ‚in·də′pen·dənt]

(mathematics)

A subsetSof a commutative ringBis said to be algebraically independent over a subringAofB(or the elements ofSare said to be algebraically independent overA) if, whenever a polynominal in elements ofS, with coefficients inA, is equal to 0, then all the coefficients in the polynomial equal 0.

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