### Abstract

For convenience, a ring with units satisfying a group identity will be called a GI-ring. We show that GI-rings have the following properties which are also properites of PI-rings. (1) Any GI-ring is Dedekind finite (von Neumann finite). (2) Nilpotent elements of a semiprimitive GI-ring have bounded index. (3) The Kurosh problem has a positive answer for GI-algebras, namely, any algebraic GI-algebra is locally finite. We also study Hartley's problem for algebraic GI-algebras.

Original language | English |
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Pages (from-to) | 226-235 |

Number of pages | 10 |

Journal | Journal of Algebra |

Volume | 232 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 Oct 1 |

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### Keywords

- Algebraic algebras
- Dedekind finite
- Group identities
- Kurosh problem
- Matrix units
- Polynomial identities
- Semiprimitive rings
- semiprime rings

### ASJC Scopus subject areas

- Algebra and Number Theory