| Factor-nilpotent Ideal of Rings |
| Received:December 26, 1990 |
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| Abstract: |
| Let n be a ring. A left (right) ideal A of ft is called factor-nilpotent if there is a positive integer m = m(r) with Amr = {0} for every element r ∈Ω. A left ideal L of Ω is called a left factor for an element b ∈Ω, if Lb ≠ {0}.Ω is called a ring with locally minimum condition for left factors, if in fl every descending chain of left factors for the same element is finite. Here we show that1 Let R be a factor-nilpotent right ideal of Ω. Then R + ΩR is a factor-nilpotent ideal of Ω.2 Let Ω be a ring with locally minimum condition of left factors. Then every nil left ideal of Ω is a factor-nilpotent left ideal. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1993.01.024 |
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