Artin published [1] on the related Wedderburn theorem, but Zorn does not cite a publication on the theorem he attributes to Artin in his 1930 paper [2]. Moufang [3] also cites Zorn in her 1935 publication on Artin's theorem as the only published source.

As discussed here, Zorn was Artin's Ph.D. student in Hamburg, Zorn's 1930 Ph.D thesis was on alternative algebras. The absence of a publication by Artin suggests Zorn credited Artin with the theorem because of a private communication between student and advisor.

[1] E. Artin, *Zur Theorie der hyperkomplexen Zahlen*, Abh. Math. Sem. Univ. Hamburg **5** (1927), 251–260.

[2] M. Zorn, *Theorie der alternativen Ringe*, Hamb. Abhandl. **8** (1930), 142-147.

[3] R. Moufang, *Zur Struktur von Alternativkörpern*, Mathem. Ann. **110** (1935), 416-430.

*Follow up after comments on the relation between Artin's theorem and the Artin-Zorn theorem:* The theorem which Zorn attributes to Artin, that in an alternative ring the subring generated by any two elements is associative, is not limited to finite rings, only the corollary, now known as the Artin-Zorn theorem is. I quote from Zorn's 1930 paper:

Herr Artin, der diese Arbeit veranlaßt hat, hat auch einen Teil der
Ergebnisse, wie die Existenz des Einheitselements und die
Reduzibilität in einfache Systeme unter der Annahme, das das
halbeinfache System über einem Grundkörper der Charakteristik Null
endlich ist, bewiesen, ferner den schönen Satz, daß ein aus zwei
Elementen erzeugtes alternatives System assoziativ ist, mit der
interessanten Folgerung: Ein nullteilerfreies alternatives System mit
endlich vielen Elementen ist Galoisfeld. Darüber hinaus bin ich ihm
für viele Hinweise und Ratschläge zu Dank verpflichtet.

_{
Mr. Artin, who prompted this work, also proved part of the results, such as the existence of the identity element and the reducibility to simple systems under the assumption that the semisimple system over a ground field of characteristic zero is finite, as well as the beautiful theorem that an alternative system generated by two elements is associative, with the interesting corollary: A zero-divisor-free alternative system with finitely many elements is a Galois field. Furthermore, I am indebted to him for many suggestions and advice.}