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Contributions to NoncommutativeIdeal Theory

Published online by Cambridge University Press:  20 November 2018

D. C. Murdoch
D. C. Murdoch*
Affiliation:
The University of British Columbia
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The well-known results of Krull concerning the minimal prime divisors and the radical of an ideal in a commutative ring have been extended to the noncommutative case in a recent paper [5] by N. H. McCoy. In that paper systematic use was made of the concept of an m-system, a set M of elements of the ring such that if a ∈ M and b ∈ M then axb ∈ M for some element x of the ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 43 - 57
Copyright
Copyright © Canadian Mathematical Society 1952

References

1. Fitting, H., Primarkomponentenzerlegung in nichtkommutativen Ringen, Math. Ann., vol. 3 (1935), 19–41.Google Scholar
2. Krull, W., Zur Theorie der zweiseitigen Ideale in Nichtkommutativen Bereichen,Math. Zeit., vol. 29 (1938), 42–54.Google Scholar
3. Krull, W., Idealtheorie in Ringen ohne Endlichkeitsbedingung,Math. Ann., vol. 101 (1929), 729–744.Google Scholar
4. Krull, W., Idealtheorie, Ergebnisse der Mathematik, vol. 4 (Berlin, 1935).Google Scholar
5. McCoy, N. H., Prime ideals in general rings, Amer. J. Math., vol. 71 (1949), 823–833.Google Scholar
6. McCoy, N. H., Rings and ideals, Carus Mathematical Monographs, No. 8 (Baltimore, 1948).Google Scholar