Right alternative rings

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...

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.

Some Questions concerning Alternative Rings

3 0 Ju l 2 00 5 STRONGLY RIGHT ALTERNATIVE RINGS AND BOL LOOPS

We partially answer two questions of Goodaire by showing that in a finite, strongly right alternative ring, the set of units (if the ring is with unity) is a Bol loop under ring multiplication, and the set of quasiregular elements is a Bol loop under " circle " multiplication. A magma (L, ·) is a set L with a binary operation · : L × L → L. A magma (L, ·) is a loop if there is a neutral element...