In [5] Tsai defined the
Brown-McCoy prime radical for Jordan rings in terms of the quadratic operation and
proved basic results for the radical. In this paper we give a definition of the prime
radical for arbitrary nonassociative rings in terms of a ⋆-operation defined on the
family of ideals and of a function f of the ring into the family of ideals in the ring.
The prime radical for Jordan or standard rings is obtained by a particular choice
of the.k-operation and the function f. We also extend the results for the
Jordan case to weakly W-admissible rings which include the generalized
standard rings and therefore alternative and standard rings as well as Jordan
rings.
