### 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 |
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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 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

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

**On nil subsemigroups of rings with group identities.** / Beidar, K. I.; Ke, Wen Fong; Liu, Chia-Hsin.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 30, no. 1, pp. 347-352. https://doi.org/10.1081/AGB-120006495

}

TY - JOUR

T1 - On nil subsemigroups of rings with group identities

AU - Beidar, K. I.

AU - Ke, Wen Fong

AU - Liu, Chia-Hsin

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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 Bd 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.

AB - 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 Bd 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.

UR - http://www.scopus.com/inward/record.url?scp=0036003478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036003478&partnerID=8YFLogxK

U2 - 10.1081/AGB-120006495

DO - 10.1081/AGB-120006495

M3 - Article

AN - SCOPUS:0036003478

VL - 30

SP - 347

EP - 352

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 1

ER -