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Quotient Rings of Noncommutative Rings in the First Half of the 20th Century

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Abstract.

A keystone of the theory of noncommutative noetherian rings is the theorem that establishes a necessary and sufficient condition for a given ring to have a quotient ring. We trace the development of this theorem, and its applications, from its first version for noncommutative domains in the 1930s to Goldie’s theorems in the late 1950s.

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  1. Departamento de Ciência da Computação, Instituto de Matemática Universidade, Federal do Rio de Janeiro, P.O. Box 68530, 21945-970, Rio de Janeiro, RJ Brazil

    S. C. Coutinho

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Correspondence to S. C. Coutinho.

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Communicated by  J. Gray

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Coutinho, S. Quotient Rings of Noncommutative Rings in the First Half of the 20th Century. Arch. Hist. Exact Sci. 58, 255–281 (2004). https://doi.org/10.1007/s00407-003-0075-0

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