[2] Ibragimov shared first place with Vladimir Kramnik and Andrei Kharlov at the 1991 USSR Under-26 Championship.

Ibragimov won the Chigorin Memorial in 1994 and the Biel Masters Open tournament in 1997.

In 2002 he started to play for the United States,[3] where he lived in New Haven, Connecticut.

Ibragimov played for the US team that took the bronze medal in the 2006 Chess Olympiad.

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