Some commutativity theorems for $s$-unital rings with constraints on commutators

H.A.S. Abujabal and V. Peri\'c

Abstract: 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 non-negative 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

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