Right alternative division 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...

The Structure of Alternative Division Rings.

1. Introduction. A ring R is said to be alternative if (xx)y = x(xy), (yx)x=y(xx) for all x, y of R. And R is a division ring if it has a non-zero element and the equations ax = b, ya = b have unique solutions x, y for a ^0; the existence of a unit is not postulated. Let R be an alternative ring without divisors of zero.1 If a, b are nonzero elements of R and m is a rational integer, the equati...

Triangulaizability of Algebras Over Division Rings

Power-associative Rings of Characteristic Two