Geodesic
Generalized n-Like Rings and Commutativity
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 449-452

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

This note continues the investigation of those rings R with unity which also satisfy the polynomial identity B(x, y) = (xy)n -xyn -xny +xy = 0, for some integer n > l. It is shown that when n is an even integer, or when n = 3, such rings are commutative. It is otherwise possible, as is shown by example, for such rings to fail to be commutative, although they are subdirect sums of local rings satisfying the polynomial identity. Each such ring has nilpotent commutator ideal. 
Moore, H. G. Generalized n-Like Rings and Commutativity. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 449-452. doi: 10.4153/CMB-1980-066-8
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[2] 2. Moore, H. G. and Yaqub, Adil, “On the Commutator Ideal of Certain Rings” Port. Math. 29 (1970) 119-124. Google Scholar

[3] 3. Moore, H. G. and Yaqub, Adil “Equational Definability of Addition in Certain Rings” Pac. J. of Math. 74 (1978) 407-417. Google Scholar

[4] 4. Yaqub, A., “A Generalization of Certain Rings of A. L. Foster,” Canad. Math. Bull. 6 (1963) 55-60. Google Scholar

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