A commutativity theorem for associative rings
Ashraf, Mohammad
Archivum Mathematicum, Tome 031 (1995), p. 201-204 / Harvested from Czech Digital Mathematics Library
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Let $m > 1, s\geq 1$ be fixed positive integers, and let $R$ be a ring with unity $1$ in which for every $x$ in $R$ there exist integers $p = p(x) \geq 0, q = q(x) \geq 0, n = n(x) \geq 0, r = r(x) \geq 0 $ such that either $ x^{p}[x^{n},y]x^{q} = x^{r}[x,y^{m}]y^{s} $ or $ x^{p}[x^{n},y]x^{q} = y^{s}[x,y^{m}]x^{r} $ for all $ y \in R $. In the present paper it is shown that $R$ is commutative if it satisfies the property $Q(m)$ (i.e. for all $x,y \in R, m[x,y] = 0$ implies $[x,y] = 0$).

Publié le : 1995-01-01
Classification:  16R50,  16U70,  16U80 
@article{107540,
     author = {Mohammad Ashraf},
     title = {A commutativity theorem for associative rings},
     journal = {Archivum Mathematicum},
     volume = {031},
     year = {1995},
     pages = {201-204},
     zbl = {0839.16030},
     mrnumber = {1368258},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107540}
}

Ashraf, Mohammad. A commutativity theorem for associative rings. Archivum Mathematicum, Tome 031 (1995) pp. 201-204. http://gdmltest.u-ga.fr/item/107540/

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