Geodesic
On Rings with Polynomial Identity xn-x=0
Publications de l'Institut Mathématique, _N_S_34 (1983) no. 48, p. 165 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

If $R\not=0$ is an associative ring with the polynomial identity $x^n-x=0$, where $n>1$ is a fixed natural number, then it is well known that $R$ is commutative. It is also known that any anti-inverse ring $R(\not=0)$ satisfies the polynomial identity $x^3-x=0$ [1]. The structure of anti-inverse rings was described in [2]: they are exactly subdirect sums of $GF(2)$'s and $GF(3)$'s. In generalizing the last result, we prove here that a ring $R$ with the polynomial identity $x^n-x=0(>1)$ is a subdirect sum of $GF(p)$'s, where $p^r-1$ divides $n-1$. We also prove again some known results about commutative regular rings.
Classification : 16A38
Keywords: Anti-inverse rings, polynomial identity $x^n-x=0$, subdirect sum of $GF(p)$'s, commutative regular rings 
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     author = {Veselin Peri\'c},
     title = {On {Rings} with {Polynomial} {Identity} xn-x=0},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {165 },
     publisher = {mathdoc},
     volume = {_N_S_34},
     number = {48},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1983_N_S_34_48_a24/}
}
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Veselin Perić. On Rings with Polynomial Identity xn-x=0. Publications de l'Institut Mathématique, _N_S_34 (1983) no. 48, p. 165 . http://geodesic.mathdoc.fr/item/PIM_1983_N_S_34_48_a24/