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 |
|---|---|
| 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
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Gamma-rings and multiplications on abelian groups. / Snyders, A. J M; Veldsman, S.
In: Communications in Algebra, Vol. 20, No. 12, 01.01.1992, p. 3741-3757.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:84935499748
VL - 20
SP - 3741
EP - 3757
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 12
ER -