On commutativity of rings with constraints involving a nil subset
DOI:
https://doi.org/10.22199/S07160917.1996.0001.00005Keywords:
Comrnutativity, Ring with identity, S-unítal ringsAbstract
The main theorem of this paper is that a ring R with unity is commutative if and only if there is a nil subset B of R such that
l. for each x ? R, either x ? Z(R) or there is a polynormial f over Z with x - x2f (x) ? B;
2. for each x, y x ? R, there are non-negative integers n > 1, m, r, s depending on a pair of ring elements x,y with x(xmy ± xrynxs) - (xmy ± xrynxs)x = 0.
A related result for a nil commutative subset of R is given and the restrictions on the hypothesis of our result are justified by examples.
References
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