Investigating a claim for Russian priority in the abstract definition of a ring

Abstract

In this article, I scutinize an assertion that the Russian-Ukrainian mathematician S O Shatunovskii (1859–1929) should be credited with the first modern definition of a ring. Shatunovskii’s claim is compared with that of Abraham Fraenkel, who defined a notion very close to the current concept of a ring in a paper of 1914.

Notes

¹There is a small amount of confusion surrounding the date of publication of Shatunovskii’s work, since no date is given on the book itself. Some online catalogues list it as having been published in 1920, but I choose to follow Sushkevich’s dating of 1917; this certainly appears to be the date of the dissertation from which the book derives.

²Subsequent writers in Russian rejected Shatunovskii’s Latinate ‘корпус’ in favour of a native Russian word, though consensus was not immediate, with both ‘поле’ (‘field’) and ‘тело’ (‘body’) being used for a time. In modern mathematical Russian, it is the former that has been retained as the term for a field, whilst the latter now denotes a ‘skew field’: a system that satisfies all the postulates of a field, except, perhaps, commutativity of multiplication. An early example of the use of ‘поле’ for ‘field’ appears in Shatunovskii’s later textbook Introduction to analysis (Shatunovskii 1923, 2), though it still denotes there a field containing the rationals, rather than an abstract field.