Ore extensions satisfying a polynomial identity

Details Ore extensions satisfying a polynomial identity Ore extensions satisfying a polynomial identity

2007-07-02

arxiv.org/abs/0707.0173v1

Journal of Algebra and Its Applications 5 No.3 (2006), pp.287-306

Mathematics

Rings and Algebras

23 pages

Scientific paper

Necessary and sufficient conditions for an Ore extension $S=R[x;\si,\de]$ to be a {\rm PI} ring are given in the case $\si$ is an injective endomorphism of a semiprime ring $R$ satisfying the {\rm ACC} on annihilators. Also, for an arbitrary endomorphism $\tau$ of $R$, a characterization of Ore extensions $R[x;\tau]$ which are {\rm PI} rings is given, provided the coefficient ring $R$ is noetherian.

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