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Jacobi and Kummer’s ideal numbers. (English)
Abh. Math. Semin. Univ. Hamb. 79, No. 2, 165-187 (2009).
The paper is devoted to the history of introducing ideal numbers by Kummer. The author begins by giving a brief summary of Jacobi’s lectures on number theory and cyclotomy which played an important role in the development of Kummer’s notion of an ideal number. Further the role of Fermat’s Last Theorem in Kummer’s work is discussed and “Jacobi maps” ‒ that turned out to be the key idea used by Kummer ‒ are presented. It is also shown how Kummer’s ideal numbers can be translated into the modern mathematical language. The paper is finished by discussing the relevance of integral closure for Kummer’s work.
Reviewer: Roman Murawski (Poznań)
Classification: A30 F60
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