In 1964 he successfully defended his PhD thesis "Decidable and Undecidable Theories" (advisor Anatoly Maltsev).

In 1966 he successfully defended his DrSc thesis "Elementary Theory of Fields" (Элементарные теория полей).

Apart from being a mathematician, Yershov was a member of the Communist Party and had different distinguished administrative duties in Novosibirsk State University.

Yershov has been accused of antisemitic practices, and his visit to the U.S. in 1980 drew public protests by a number of U.S.

He proved decidability of the elementary theory of the field of p-adic numbers (independently proven by J.