Centers of alternative rings

On Rings with Prime Centers

Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of prime centers to commutativity. An example of a non-commutative ring with a prime center is given.

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.

Neumann Near-rings and Neumann Centers

We study near-rings N with the property (∗) : xS = Sx for each x ∈ N and each n-subset S of N . By localizing (∗), we obtain center-like subsets, which we study for the case of rings. In response to a question of B.H. Neumann, we defined a Qn–ring to be a ring R with the property that xS = Sx for all x ∈ R and all n-subsets S of R. In [3] we investigated basic properties of Qn–rings and establi...

Some Questions concerning Alternative Rings

Right Alternative Division Rings of Characteristic Two