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Commutativity results for rings with certain constraints on commutators

Author
Abujabal, Hamza A. S.

Peric, Veselin

Full text
http://www.revistaproyecciones.cl/article/view/2694
10.22199/S07160917.1995.0001.00003
Abstract
We investigate here the commutativity of a left (resp. right) s-unital ring R satisfying the polynomial identity yr [xny] xt = ±y3 [x, ym] (resp. yr [xn, y] xt = ± [x, ym] ys ) for some non-negative integers m >0, n > 0, r, s and t such that n + t > 1 (resp. m + s > 1 for r = 0). For such a ring R, we prove the commutativity if n + t > 1, and the commutators in R are n-torsion free (Q (n) property) for m > 1, n > 1, and ( t + 1)-torsion free for n = 1 (and t > 0). lf r = 0, then R is commutative provided m+ s > 1 and R has Q (m) property for m > 1, n > 1, and Q (s + 1) property for m = 1 (and s > 0). Especially, for r = 0, R is commutative, if m and n are relatively prime integers (not both equal to one).
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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