Local near-rings with commutative groups of units (Q2705845)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local near-rings with commutative groups of units |
scientific article |
Statements
19 March 2001
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local nearrings
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groups of units
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Local near-rings with commutative groups of units (English)
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Properties of a local (right) nearring \(N\) with commutative group \(N^*\) of units are studied. The author proves that in such a nearring the subgroup \(L\) of elements with no left inverses is an ideal of \(N\) and either \(N^+\) is Abelian or \(L^+\) is Abelian and \(N/L\) is \(\text{GF}(2)\). Moreover, \(N^+\) is finitely generated iff \(L^+\) is finitely generated iff the group \(N^*\) is finitely generated. Local nearrings with a cyclic group of units are explicitly given.
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