Consider the complex numbers C as a module over integers Z, and let a be a complex number.

Consider the subset W_a = {1,a,a^2,...,a^n,...}

of the Z-module C. Then I want to show that

W_a is linearly independent iff a is a transcedent number.

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- February 4th 2009, 04:47 AMpeteryellowthe complex numbers C as a module over integers Z
Consider the complex numbers C as a module over integers Z, and let a be a complex number.

Consider the subset W_a = {1,a,a^2,...,a^n,...}

of the Z-module C. Then I want to show that

W_a is linearly independent iff a is a transcedent number. - February 4th 2009, 05:47 PMNonCommAlg