### 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 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

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

**Gamma-rings and multiplications on abelian groups.** / Snyders, A. J M; Veldsman, S.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 20, no. 12, pp. 3741-3757. https://doi.org/10.1080/00927879208824539

}

TY - JOUR

T1 - Gamma-rings and multiplications on abelian groups

AU - Snyders, A. J M

AU - Veldsman, S.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84935499748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84935499748&partnerID=8YFLogxK

U2 - 10.1080/00927879208824539

DO - 10.1080/00927879208824539

M3 - Article

VL - 20

SP - 3741

EP - 3757

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 12

ER -