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This question already has an answer here:

What was the motivation to use the word "kernel" in algebra to denote the set of all arguments which are mapped to the idendity element (by a homomorphism)? Who introduced it?

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marked as duplicate by VicAche, Alexandre Eremenko, Logan M Apr 21 '17 at 19:36

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Source: Mathwords

KERNEL ... The use of kernel in algebra appears to be unrelated to its use in integral equations and Fourier analysis. The OED gives the following quotation from Pontrjagin’s Topological Groups i. 11 (translated by E. Lehmer 1946) "The set of all the elements of the group G which go into the identity of the group G* under the homomorphism g is called the kernel of this homomorphism."

Kern used this way (the set of elements of a group mapped to the identity by a homomorphism) is in my German-language copy of van der Waerden Algebra.

Ziegler points out some earlier uses HERE.

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    $\begingroup$ What year is your German van der Waerden? Kernel appears in the 1970 English translation of the seventh edition (1966), but not in the 1949 English translation of the second edition (1937). $\endgroup$ – Francois Ziegler Apr 5 '17 at 6:07
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    $\begingroup$ @FrancoisZiegler ... interesting. Mine is the 1966 German edition. So Pontryagin may really be the first time? $\endgroup$ – Gerald Edgar Apr 5 '17 at 13:17
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    $\begingroup$ No, Pontryagin's book isn't the first either — see details at the question of which this is a duplicate. $\endgroup$ – Francois Ziegler Apr 5 '17 at 13:23

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