摘要
Γ-环是一个比环更广泛的代数系统,它的定义可以在文献[1]中找到.S.Kyuno把Γ-域定义为左算子环是除环,有单位元的交换Γ-环,并证明了:不含非零幂零元的亚直接不可约交换Γ-环必为Γ-域.本文将减弱交换性的条件而得出相应的结果,从而把S.Kyuno定理进行了推广.
A left ideal L of a Г-ring M is called left symmetric if aabβb∈L implies where a,b, c∈ M, a ,β∈Γ. A Γ-ring M is called to be a Γ-division ring if it has the left unity, and if left oprator ring R is a division ring.In this paper, the following results are pvoved:Suppose that every left ideal of a Γ-ring M is left symmetiic.If A is subdirectly irreducible with more than one element and with no nonzero nilpotents then it is a Γ-division ring.If M is subdirectly irreducible and if D≠M then M/D is a Γ-division ring where D= (a∈M\aΓb =0,0≠b∈m)
