Right alternative rings of characteristic two

Right Alternative Division Rings of Characteristic Two

Right Alternative Rings of Characteristic Two

for all w, x, y and showed by example that (1.1) can fail to hold. Prior to this, Kleinfeld [l ] generalized the Skornyakov theorem in another direction by assuming only the absence of one sort of nilpotent element. We now specify Kleinfeld's result in detail. Let F be the free nonassociative ring generated by Xi and x2 and suppose that R is any right alternative ring. Kleinfeld calls t, u, v i...

Power-associative Rings of Characteristic Two

Noncommutative rings and characteristic classes of foliations

The notion of a characteristic fibration is introduced. This fibration consists of a base space M and a set of fibres which are dimension groups associated to a noncommutative ring R. Every dimension group of the fibration is isomorphic to the first Betti group of M with a ‘positive cone’ depending continuously on the fibre. The characteristic fibrations are linked to the codimension–1 regular ...

Alternative Loop Rings

DRAFT Abstract The right alternative law implies the left alternative law in loop rings of characteristic other than 2. We also exhibit a loop which fails to be a right Bol loop, even though its characteristic 2 loop rings are right alternative.