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Goursat's Theorem and Homological Algebra

Published online by Cambridge University Press:  20 November 2018

Joachim Lambek
Joachim Lambek*
Affiliation:
McGill University
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This expository note consists of two parts: In the first we present a homological formulation of Goursat's theorem. In the second we indicate how some rudimentary concepts of homological algebra can be introduced with the help of this form of Goursat's theorem. The second part is addressed to those readers with an algebraic background who wish to be initiated into homological algebra as painlessly as possible. The ideas developed here are close to the spirit of [5, Chapter II, § 6], where further references may be found. In fact, these ideas are very much in the air, and any originality in the present note is purely coincidental.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 4 , December 1964 , pp. 597 - 608
Copyright
Copyright © Canadian Mathematical Society 1964

References

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3. Goursat, É., Sur les substitutions orthogonales …, Ann. Sci. Éc. Norm. Sup. (3), 6(1889), 9–102.CrossRefGoogle Scholar
4. Lambek., J., Goursat's Theorem and the Zassenhaus Lemma, Can. J. Math. 10(1958), 45–56.CrossRefGoogle Scholar
5. MacLane., S., Homology, New York 1963.CrossRefGoogle Scholar
6. Shoda., K., Allgemeine Algebra, Osaka Math. J. 2 (1949), 182–225.Google Scholar