A result On Rings of type (p,q,r) = (r,q,p)

Abstract

A non-associative ring with (p,q,r) = (r,q,p) is called as an  antiflexible ring. Some other interesting non-associative rings are Assosymmetric, Accessible, Alternative, Novikov and flexible rigs. By nature, Nucleus N_u is an associator whereas Center C_e is a commutator. Moreover nucleus is not equal to center in any non-associative rings. Let us take a non- associative 2 divisible simple ring A with (p,q,r) = (r,q,p)  which is neither  associative nor commutative. In this paper it will be established first that  “ Nucleus of A commutes with every associator of A” . With the help of this property, a well known another property " Every associator is in the nucleus of Antiflexible ring" will be obtained and finally  N_u = C_e will be proved in simple antiflexible rings