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A generalization of additive ideal theory

Published online by Cambridge University Press:  24 October 2008

P. M. Grundy
P. M. Grundy
Affiliation:
Clare CollegeCambridge
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Extract

The division of ideal theory into the additive and multiplicative branches of the subject is a marked one of long standing. It is the object of this paper to carry the distinction a stage further, by showing how the group-theoretic methods of the additive branch can be extended to modules, that is, to Abelian groups, provided the ring of operators is commutative.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 3 , July 1942 , pp. 241 - 279
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

REFERENCES

Krull, W. Idealtheorie. Ergebnisse der Math. 4, Heft 3.Google Scholar
van der Waerden, B. L.Moderne Algebra, 1, 2 (1st ed.). Die Grundlehren der mathe-matischen Wissenschaften, 33, 34.Google Scholar
Birkhoff, G. (1). Lattice Theory. American Math. Soc. Colloquium Publications, no. 25.Google Scholar
Fitting, H. (1). Primärkomponentenzerlegung in nichtkommutativen Ringen. Math. Ann. 111 (1935), 19–41.CrossRefGoogle Scholar
Grell, H. (1). Beziehungen zwischen den Idealen verscheidener Ringe. Math. Ann. 97 (1927), 490–523.CrossRefGoogle Scholar
Gröbner, W. (1). Über irreduzible Ideale in kommutativen Ringen. Math. Ann. 110 (1934), 197–222.CrossRefGoogle Scholar
Krull, W. (1). Ein neuer Beweis für die Hauptsätze der allgemeinen Idealtheorie. Math. Ann. 90 (1923), 55–64.CrossRefGoogle Scholar
(2)Axiomatische Begründung der allgemeinen Idealtheorie. Sitzungsber. Phys.-med. Soz. Erlangen, 56 (1924), 47–63.Google Scholar
(3)Primidealketten in allgemeinen Ringbereichen. Sitzungsber. Heidelberger Akad. Wiss., Math.-naturwiss. Klasse, 1928, 7. Abhandlung.Google Scholar
(4)Zweiseitige Ideale in nichtkommutativen Bereichen. Math. Z. 28 (1928), 481–503.CrossRefGoogle Scholar
Lasker, E. (1). Zur Theorie der Moduln und Ideale. Math. Ann. 60 (1905), 20–116.CrossRefGoogle Scholar
Macaulay, F. S. (1). The Algebraic Theory of Modular Systems. Cambridge Tracts in Mathematics and Mathematical Physics, no. 19.Google Scholar
Noether, E. (1). Idealtheorie in Ringbereichen. Math. Ann. 83 (1921), 24–66.CrossRefGoogle Scholar
(2)Hyperkomplexe Grössen und Darstellungstheorie. Math. Z. 30 (1929), 641–692.CrossRefGoogle Scholar
van der Waerden, B. L. (1). Eine Verallgemeinerung des Bézoutschen Theorems. Math. Ann. 99 (1928), 497–541.CrossRefGoogle Scholar