In 1986, Frolov participated in the individual semi-finals of the USSR Chess Championship.

In 1990, he shared 3rd place (behind Boris Alterman, together with Vladimir Kramnik) in the final of the USSR Junior Chess Championship in the U20 age group.

In 1991 he participated in the last final of the individual USSR Chess Championship, scoring 6½ points in 11 games.

[1] Frolov started competing in international chess tournaments at the end of the 1990s, achieving a number of successes, including 1st place in Trnava (1989, tournament C), 1st place in Siófok (1990, together with István Csom), 2nd place in Alushta (1992, after Igor Novikov), shared 1st place in Mykolaiv (1993, zonal tournament, together with Aleksej Aleksandrov; in playoff Artur Frolov won 1½:½ and advanced to the tournament played in the same year in Biel Interzonal chess tournament, in which he was unsuccessful, taking a distant place,[2]) 1st place in Groningen (1993), shared 1st place in Hlohovec (1993) and 2nd plce in Pula (1994, after Vladimir Tukmakov, together with Gyula Sax, Stanislav Savchenko, Mišo Cebalo and Krunoslav Hulak).

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