Kolmogorov invited Malcev to join his graduate programme at Moscow University, and he held a studentship there for a year although he continued his teaching post at the Ivanovo Pedagogical Institute during the year. Malcev always considered himself to have been Kolmogorov 's student and certainly during the year he held the studentship at Moscow University, Malcev was directed by Kolmogorov to certain algebra problems.
Kolmogorov inimbitahan Malcev na sumali sa kanyang mga nagtapos ng programa sa Moscow University, at siya ay may hawak na isang taon para sa isang taon kahit na siya ang patuloy na kanyang pagtuturo post sa Ivanovo paturo Institute sa panahon ng taon. Malcev laging isinasaalang-alang sa sarili ay Kolmogorov 's mag-aaral at tiyak sa panahon ng taon na siya hawak ng taon sa Moscow University, Malcev ang by Kolmogorov sa tiyak na algebra problema.