On separable extensions of group rings and quaternion rings

George Szeto
1978 International Journal of Mathematics and Mathematical Sciences  
The purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extensionRG(Rmay be a non-commutative ring), and (2) to give a full description of the set of separable idempotents for a quaternion ring extensionRQover a ringR, whereQare the usual quaternionsi,j,kand multiplication and addition are defined as quaternion algebras over a field. We shall show thatRGhas a unique separable idempotent if
more » ... d only ifGis abelian, that there are more than one separable idempotents for a separable quaternion ringRQ, and thatRQis separable if and only if2is invertible inR.
doi:10.1155/s0161171278000435 fatcat:xdbbak4owjgl5n47ttq4sl6q2m