On uniform ideals and finite Goldie dimension in $R$-groups
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Keywords:
Nearring, essential ideal, uniform ideal, finite dimensionAbstract
We consider an $R$-group $G$, where $R$ is a (right) nearring. We introduce the notions relative uniform and strictly relative uniform ideals (or $R$-subgroup) which are not uniform, in general. We prove important properties and obtain a characterization for an $R$-subgroup to have finite Goldie dimension, in terms of strictly relative uniform $R$-subgroups. We provide the necessary examples.
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