Vol. 75, No. 1, 1978

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On prime gamma rings

Shoji Kyuno

Vol. 75 (1978), No. 1, 185–190

The notion of a Γ-ring was introduced by N. Nobusawa. The class of Γ-rings contains not only all rings but also Hestenes ternary rings. Recently, W. E. Barnes, J. Luh, W. E. Coppage and the author studied the structure of Γ-rings and obtained various generalizations analogous of corresponding parts in ring theory. The object of this paper is to study the properties of prime Γ-rings. Main results are the following theorems: (1) A Γ-ring M is a subdirect sum of prime Γ-rings if and only if 𝒫(M) = 0, where 𝒫(M) denotes the prime radical of M. (2) For the matrix Γn,m-ring Mm,n we have 𝒫(Mm,n) = (𝒫(M))m,n, where M is a ring such that x MΓxΓM for every x M.

Mathematical Subject Classification
Primary: 16A78, 16A78
Received: 9 March 1977
Published: 1 March 1978
Shoji Kyuno