Simple locally (-1,1) nil rings
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.
scientific article; zbMATH DE number 3944107