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Investigating a claim for Russian priority in the abstract definition of a ring. (English) Zbl 1293.01012

This article deals with definitions of abstract rings in particular in the work of Shatunovskij. Definitions of “ring-like” objects began to appear at the beginning of the 20th century in J. König’s book [Einleitung in die allgemeine Theorie der algebraischen Größen. Leipzig: B. G. Teubner (1903; JFM 34.0093.02)], in A. Fraenkel’s work [J. Reine Angew. Math. 141, 43–76 (1912; JFM 43.0269.01)], and in Shatunovskij’s dissertation [Algebra as the study of congruences by functional moduli (Russian) (1917)]. The most influential work on abstract rings was certainly E. Noether’s paper [Math. Ann. 83, 24–66 (1921; JFM 48.0121.03)] from 1921: this article became widely studied after Noether had succeeded in giving an axiomatic definition of what we now call Dedekind rings [E. Noether, Math. Ann. 96, 26–61 (1926; JFM 52.0130.01)].

MSC:

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
13-03 History of commutative algebra
16-03 History of associative rings and algebras
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