# Origin of the modern definition of the tensor product

Due to whom is the modern (i.e. via its universal property) definition of the tensor product, and in which article was it communicated?

-

My recollection agrees with Mariano. Here's an except from Weibel's History of homological algebra

and from p. 172 of Mac Lane's Homology

and from Whitney's Collected Papers v. 1

-
what is the reference B43 which is quoted in the weibel's book? – PtF Dec 19 '14 at 23:32
@PtF R. Baer, Erwiterung von Gruppen und ihren Isomorphismen, Math. Zeit. 38 (1934), 375-416. Note that I added a link to an online source of Weibel's paper. – Bill Dubuque Dec 19 '14 at 23:42
Thanks and I apologize myself for not seeing the link.. – PtF Dec 20 '14 at 12:41

The article

Whitney, Hassler. Tensor products of Abelian groups. Duke Mathematical Journal 4 (1938), no. 3, 495--528.

is usually credited as the original source.

Very soon after that, Bourbaki crystallized the modern definition.

-
I don't seem to be able to find that paper free online, which is sad. – Mariano Suárez-Alvarez Jan 18 '14 at 20:23
If someone wants a copy of Whitney's paper I can send it by mail. You can contact me at my first.lastname at gmail.com – Bill Dubuque Jan 18 '14 at 20:55