## Abstract

A ring R is called an E-ring if every endomorphism of R^{+}; the additive group of R; is multiplication on the left by an element of R: This is a well known notion in the theory of abelian groups. We want to change the “E” as in endomorphisms to an “A” as in automorphisms: We define a ring to be an A-ring if every automorphism of R^{+} is multiplication on the left by some element of R: We show that many torsion-free finite rank (tffr) A-rings are actually E-rings. While we have an example of a mixed A-ring that is not an E-ring, it is still open if there are any tffr A-rings that are not E-rings. We will employ the Strong Black Box [5] to construct large integral domains that are A-rings but not E-rings.

Original language | English |
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Pages (from-to) | 277-292 |

Number of pages | 16 |

Journal | Colloquium Mathematicum |

Volume | 96 |

Issue number | 2 |

DOIs | |

State | Published - 2003 |

### Bibliographical note

Publisher Copyright:© 2003, Instytut Matematyczny. All rights reserved.