PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 34(48), pp. 165167 (1983) 

ON RINGS WITH POLYNOMIAL IDENTITY $x^nx=0$Veselin Peri\'cPrirodnomatematicki fakultet, Sarajevo, YugoslaviaAbstract: If $R\not=0$ is an associative ring with the polynomial identity $x^nx=0$, where $n>1$ is a fixed natural number, then it is well known that $R$ is commutative. It is also known that any antiinverse ring $R(\not=0)$ satisfies the polynomial identity $x^3x=0$ [1]. The structure of antiinverse 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 $x^nx=0(>1)$ is a subdirect sum of $GF(p)$'s, where $p^r1$ divides $n1$. We also prove again some known results about commutative regular rings. Keywords: Antiinverse rings; polynomial identity $x^nx=0$; subdirect sum of $GF(p)$'s; commutative regular rings Classification (MSC2000): 16A38 Full text of the article:
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
