The eight lemma states that if, in the above commutative diagram of modules and module homomorphisms the columns and two upper rows are exact, then so is the bottom row.
Eight Lemma
See also
Five Lemma, Four Lemma, Nine LemmaThis entry contributed by Margherita Barile
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References
Strooker, J. R. "The Eight-Lemma." §2.6.7 in Introduction to Categories, Homological Algebra and Sheaf Cohomology Cambridge, England: Cambridge University Press, pp. 99-101, 1978.Referenced on Wolfram|Alpha
Eight LemmaCite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Eight Lemma." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EightLemma.html