algebraically independent


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algebraically independent

[¦al·jə¦brā·ik·lē ‚in·də′pen·dənt]
(mathematics)
A subset S of a commutative ring B is said to be algebraically independent over a subring A of B (or the elements of S are said to be algebraically independent over A) if, whenever a polynominal in elements of S, with coefficients in A, is equal to 0, then all the coefficients in the polynomial equal 0.
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Another approach is to assign algebraically independent values to the nonzeros (i.
1 Any maximal weakly separated subset [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] corresponds to k(n - k) +1 algebraically independent Plucker coordinates [[DELTA].
W] is again a polynomial algebra, and it can be generated by n algebraically independent homogeneous polynomials [f.