Gamma—rings and multiplications on abelian groups |
| |
Authors: | AJM Snyders S Veldsman |
| |
Institution: | Department of Mathematics , University of Port Elizabeth , Port Elizabeth, South Africa |
| |
Abstract: | If M and Γ are abelian groups, then M will be a Γ-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. |
| |
Keywords: | |
|
|