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History of Science and Engineering

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THE HISTORY OF THE CONCEPT OF «INNER IDEAL»
E.V. Mescherina

This article describes the origin and development of the concept of «inner ideal» for Jordan algebras and Lie algebras. The concept of «inner ideal» N. Jacobson introduced in 1969 [1]. This was a new concept to replace the old notion of «quadratic ideal». Jacobson introduced him to build the structure theory of quadratic Jordan algebras [2]. Subsequently, the inner ideals in Jordan algebras were used K. Maccrimmon [3] J. Faulkner [4], D. Kats [5] and others. The fi rst systematic study of the internal ideals in Lie algebras took George Benkart in 1975 [6]. Also, the study of domestic ideals Lie engaged scholars such as Antonio Fernandez Lopez, Esther Garcia, Miguel Gomez Lozano [7–10], Erhard Neher [9] Christine Draper [11], A.A. Premet [12, 13], A.A. Baranov, J. Rowley [14].
Keywords: Lie algebra; inner ideal of a Jordan algebra; inner ideal of the Lie algebra; the prime radical of the Lie algebra; solvable Lie algebra.

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