A nonidentity for 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...

A COMMUTATIVITY CONDITION FOR RINGS

In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.

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.

A Simplification of Morita’s Construction of Total Right Rings of Quotients for a Class of Rings

The total right ring of quotients Qtot(R), sometimes also called the maximal flat epimorphic right ring of quotients or right flat epimorphic hull, is usually obtained as a directed union of a certain family of extension of the base ring R. In [16], Qtot(R) is constructed in a different way, by transfinite induction on ordinals. Starting with the maximal right ring of quotients Qmax(R), its sub...