Geodesic
Rings Satisfying (x, y, z) = (y, z, x)
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 913-918

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a ring satisfying the identity 1 for all x, y, z ε R, where (x,y,z) = (xy)z — x(yz). If R also satisfies the identity (x, x, x) = 0 for all x ε R, then R is alternative. It is known that if R satisfies (1), it need not be an alternative (see 6). Thus, the class of rings satisfying (1) is a non-trivial extension of the class of alternative rings. P. Jordan remarked that (x, x, x)2 = 0 is an identity in R (see 9). 
Sterling, Nicholas J. Rings Satisfying (x, y, z) = (y, z, x). Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 913-918. doi: 10.4153/CJM-1968-088-8
@article{10_4153_CJM_1968_088_8,
     author = {Sterling, Nicholas J.},
     title = {Rings {Satisfying} (x, y, z) = (y, z, x)},
     journal = {Canadian journal of mathematics},
     pages = {913--918},
     year = {1968},
     volume = {20},
     number = {1},
     doi = {10.4153/CJM-1968-088-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-088-8/}
}
TY  - JOUR
AU  - Sterling, Nicholas J.
TI  - Rings Satisfying (x, y, z) = (y, z, x)
JO  - Canadian journal of mathematics
PY  - 1968
SP  - 913
EP  - 918
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-088-8/
DO  - 10.4153/CJM-1968-088-8
ID  - 10_4153_CJM_1968_088_8
ER  - 
%0 Journal Article
%A Sterling, Nicholas J.
%T Rings Satisfying (x, y, z) = (y, z, x)
%J Canadian journal of mathematics
%D 1968
%P 913-918
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-088-8/
%R 10.4153/CJM-1968-088-8
%F 10_4153_CJM_1968_088_8

[1] 1. Bruck, R. H. and Kleinfeld, E., The structure of alternative division rings, Proc. Amer. Math. Soc. 2 (1951), 878–890. Google Scholar

[2] 2. Kleinfeld, E., Extension of a theorem on alternative division rings, Proc. Amer. Math. Soc. 3 1952), 348–35. Google Scholar

[3] 3. Kleinfeld, E., Simple alternative rings, Ann. of Math. (2), 58 (1953), 544–547. Google Scholar

[4] 4. Kleinfeld, E., On simple alternative rings, Amer. J. Math. 75 (1953), 98–104. Google Scholar

[5] 5. Kleinfeld, E., Alternative nil rings, Ann. of Math. (2) 66 (1957), 395–399. Google Scholar

[6] 6. Kleinfeld, E., Assosymmetric rings, Proc. Amer. Math. Soc. 8 (1957), 983–986. Google Scholar

[7] 7. Outcalt, D. L., An extension of the class of alternative rings, Can. J. Math. 17 (1965), 130–141. Google Scholar

[8] 8. San Soucie, R. L. Weakly standard rings, Amer. J. Math. 79 (1957), 80–86. Google Scholar

[9] 9. Zorn, M., Alter nativkor per und quadratische Système, Abh. Math. Sem. Hamburg Univ. 9 1933), 395–402. Google Scholar

Cité par Sources :