Classification of rings satisfying some constraints on subsets
Khan, Moharram A.
Archivum Mathematicum, Tome 043 (2007), p. 19-29 / Harvested from Czech Digital Mathematics Library
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Let $R$ be an associative ring with identity $1$ and $J(R)$ the Jacobson radical of $R$. Suppose that $m\ge 1$ is a fixed positive integer and $R$ an $m$-torsion-free ring with $1$. In the present paper, it is shown that $R$ is commutative if $R$ satisfies both the conditions (i) $[x^m,y^m]=0$ for all $x,y\in R\backslash J(R)$ and (ii) $[x,[x,y^m]]=0$, for all $x,y\in R\backslash J(R)$. This result is also valid if (ii) is replaced by (ii)’ $[(yx)^mx^m-x^m(xy)^m,x]=0$, for all $x,y\in R\backslash N(R)$. Our results generalize many well-known commutativity theorems (cf. [1], [2], [3], [4], [5], [6], [9], [10], [11] and [14]).

Publié le : 2007-01-01
Classification:  16U80 
@article{108046,
     author = {Moharram A. Khan},
     title = {Classification of rings satisfying some constraints on subsets},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {19-29},
     zbl = {1156.16304},
     mrnumber = {2310121},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108046}
}

Khan, Moharram A. Classification of rings satisfying some constraints on subsets. Archivum Mathematicum, Tome 043 (2007) pp. 19-29. http://gdmltest.u-ga.fr/item/108046/

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