### Abstract

If M and Γ are abelian groups, then M will be a T—ring iff there exists a group homomorphism f from Γ into the group of all multiplications of M, Mult(M), such that f(Γ) satisfies the Generalized Associativity Property on M. In this note we examine the following special cases of this result: (i) M is a Γ—ring satisfying the Nobusawa Condition, (ii) M is a cyclic group, (iii) M is a direct sum of cyclic groups and (iv) M is a Γ-ring that has unity elements.

Original language | English |
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Pages (from-to) | 3741-3757 |

Number of pages | 17 |

Journal | Communications in Algebra |

Volume | 20 |

Issue number | 12 |

DOIs | |

Publication status | Published - Jan 1 1992 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Snyders, A. J. M., & Veldsman, S. (1992). Gamma-rings and multiplications on abelian groups.

*Communications in Algebra*,*20*(12), 3741-3757. https://doi.org/10.1080/00927879208824539