### Abstract

Let R be a unital ring satisfying a group identity. We prove that if B is a nil subsemigroup of R, then it is locally nilpotent, and B^{d} is contained in the sum of all nilpotent ideals of R, where the positive integer d is determined by the group identity. Note that the above result for PI-rings is due to Amitsur.

Original language | English |
---|---|

Pages (from-to) | 347-352 |

Number of pages | 6 |

Journal | Communications in Algebra |

Volume | 30 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 Jan 1 |

### ASJC Scopus subject areas

- Algebra and Number Theory

## Fingerprint Dive into the research topics of 'On nil subsemigroups of rings with group identities'. Together they form a unique fingerprint.

## Cite this

Beidar, K. I., Ke, W. F., & Liu, C-H. (2002). On nil subsemigroups of rings with group identities.

*Communications in Algebra*,*30*(1), 347-352. https://doi.org/10.1081/AGB-120006495