### Abstract

It is well-known that the Jacobson radical of a unital ring R is the largest superfluous right ideal of R. While a simple example shows this to be false for non-unital rings, it is shown that the result remains valid in the absence of a unit provided the notion of "superfluous" is taken relative to all regular right ideals. The purpose of this note is to provide a proof for this little-known fact.

Original language | English |
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Pages (from-to) | 4740-4742 |

Number of pages | 3 |

Journal | Communications in Algebra |

Volume | 47 |

Issue number | 11 |

Early online date | 13 Apr 2019 |

DOIs | |

Publication status | Published - 2019 |