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U.S.S.R. (Union of Soviet Socialist Republics)

A citizen of the former Soviet Union is not necessarily a Russian; be specific when the people of other republics are meant:
            Ukrainian, Kazakh, Uzbek, etc.

Do not use Soviet alone as a noun for the former Soviet Union or for individuals. Soviets (in the plural) is acceptable for the government or its people.  Soviet is the preferred adjective.

See also Commonwealth of Independent States.