Distributive elements and endomorphisms of a near-ring (Q1095999)
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scientific article; zbMATH DE number 4029782
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distributive elements and endomorphisms of a near-ring |
scientific article; zbMATH DE number 4029782 |
Statements
Distributive elements and endomorphisms of a near-ring (English)
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1988
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Let N be a right zero-symmetric near-ring with identity. In this note the following are proved to be equivalent: i) the distributive part \(N_ d\) of N is a ring; ii) \((N,+)\) is abelian; iii) the left near-ring Ass(N) associated to N is a ring. Besides N is shown to be a faithful, monogenic and unitary right Ass(N)-group whose centralizer is isomorphic to the monoid \((N_ d,\cdot)\).
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right zero-symmetric near-ring
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distributive part
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left near-ring
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centralizer
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