If algebraic integers 
, ..., 
are linearly independent over 
, then 
, ..., 
are algebraically
independent over 
. The Lindemann-Weierstrass theorem is implied by Schanuel's
conjecture (Chow 1999).
Lindemann-Weierstrass Theorem
See also
Algebraically Independent, Hermite-Lindemann Theorem, Schanuel's ConjectureExplore with Wolfram|Alpha
References
Baker, A. Theorem 2.1 in Transcendental Number Theory. Cambridge, England: Cambridge University Press, 1990.Chow, T. Y. "What is a Closed-Form Number?" Amer. Math. Monthly 106, 440-448, 1999.Referenced on Wolfram|Alpha
Lindemann-Weierstrass TheoremCite this as:
Weisstein, Eric W. "Lindemann-Weierstrass Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Lindemann-WeierstrassTheorem.html