· Portal  Help Search Members Calendar 
Welcome Guest ( Log In  Register )  Resend Validation Email 
zIFBoards gives you all the tools to create a successful discussion community.  Welcome to Did You Know? 
JaneFairfax 
Posted: 15:40 Wednesday 05 August 2009

The Enlightenment Group: Moderators Posts: 670 Member No.: 20 Joined: 03 Mar 2007 
Did you know? The Gelfond–Schneider theorem states if α is an algebraic number not equal to 0 or 1 and β is an irrational algebraic number, then A proof of this theorem is included in the chapter on transcendental numbers in the book A Course in Number Theory by H.E. Rose. 
algebraic topology 
Posted: 20:28 Wednesday 05 August 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? This theorem is a resolution of part of the seventh of the mathematical problems famously proposed by David Hilbert in 1900. 
Ebudae 
Posted: 20:44 Wednesday 05 August 2009

The Enlightenment Group: Admin Posts: 933 Member No.: 1 Joined: 02 Jan 2007 
Did you know? Schneider is the German word for a tailor.  Ebudæ

algebraic topology 
Posted: 21:48 Wednesday 05 August 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? The theorem was first proved by Aleksandr Gelfond in 1934; Theodor Schneider refined the proof in 1935. 
JaneFairfax 
Posted: 12:20 Thursday 06 August 2009

The Enlightenment Group: Moderators Posts: 670 Member No.: 20 Joined: 03 Mar 2007 
Did you know? The proof of the Gelfond–Schneider theorem given in the book by Rose goes by assuming to the contraray that α, β and 
algebraic topology 
Posted: 11:49 Thursday 27 August 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? If F is a subfield of E, a number α in E is said to be algebraic over F iff α is a root of a nonzero polynomial with coefficients in F; α is said to be transcendental over F iff it is not algebraic over F. The Gelfond–Schneider theorem is a result concerning complex transcendental numbers over the rationals. 
JaneFairfax 
Posted: 17:00 Thursday 27 August 2009

The Enlightenment Group: Moderators Posts: 670 Member No.: 20 Joined: 03 Mar 2007 
Did you know? A complex number is a root of a polynomial with rational coefficients if and only if it is a root of a polynomial with integer coefficients. This is Gauß’s lemma. 
algebraic topology 
Posted: 18:19 Thursday 27 August 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? If R is an integral domain with field of fractions F, an element in some field containing F is a root of a polynomial with coefficients in F if and only if it is a root of a polynomial with coefficients in R. For if α is a root of where 
JaneFairfax 
Posted: 09:58 Friday 28 August 2009

The Enlightenment Group: Moderators Posts: 670 Member No.: 20 Joined: 03 Mar 2007 
Did you know? If F is a subfield of E and is algebraic over F, the (unique) monic polynomial in 
algebraic topology 
Posted: 16:29 Friday 28 August 2009

Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 
Did you know? If F is a subfield of E, the elements of E which are algebraic over F form a subfield of E containing F. 