樊复生.关于亚直接不可约完全左对称Г-环[J].数学研究及应用,1991,11(1):28~30 |
关于亚直接不可约完全左对称Г-环 |
On Subdirectly Irreducible Completely Left Symmetric F-rings |
投稿时间:1989-02-23 |
DOI:10.3770/j.issn:1000-341X.1991.01.006 |
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A left ideal L of a Г-ring M is called left symmetric if aabβb∈L implies aacβb∈L, 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). |
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