Simple locally (-1,1) nil rings (Q1073169)
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scientific article; zbMATH DE number 3944107
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Simple locally (-1,1) nil rings |
scientific article; zbMATH DE number 3944107 |
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Simple locally (-1,1) nil rings (English)
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1986
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A (-1,1) ring is a right alternative ring satisfying the identity \((x,y,z)+(y,z,x)+(z,x,y)=0\), where \((x,y,z)=(xy)z-x(yz)\). A ring is called locally (-1,1) ring in case the subring generated by any two of its elements is (-1,1). This paper is devoted to the proof of the following Theorem: ''Any simple locally (-1,1) nil ring with characteristic \(\neq 2,3\) is associative.
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associativity
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Shirsov locally right nilpotent
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right alternative ring
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simple locally (-1,1) nil ring
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