PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 52(66), pp. 8694 (1992) 

Some commutativity theorems for $s$unital rings with constraints on commutatorsH.A.S. Abujabal and V. Peri\'cOdsjek za matematiku, Prirodnomatematicki fakultet, Sarajevo, Bosna i HercegovinaAbstract: Continuing the investigation of [1], [2], [3] and [10], we prove here some commutativity theorems for $s$unital rings $R$ satisfying the polynomial identity $x^t[x^n,y]y^{t'} =\pm x^{s'}[x,y^m]y^s$, resp.\ $x^t[x^n,y]y^{t'} =\pm y^s[x,y^m]x^{s'}$, where $m,n,s,s',t$ and $t'$ are given nonnegative integers such that $m>0$ or $n>0$ and $t+n\ne s'+1$ or $m+s\ne t'+1$ for $m=n$. The additional assumption in these theorems concern some torsion freeness of commutators in$R$. Keywords: Commutativity of $s$unital rings, polynomial identity, torsion freeness of commutators. Classification (MSC2000): 16A76 Full text of the article:
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