Vol. 42, No. 1, 1972

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A generalization of the prime radical in nonassociative rings

Hyo Chul Myung

Vol. 42 (1972), No. 1, 187–193

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.

Mathematical Subject Classification 2000
Primary: 17A99
Received: 19 March 1971
Revised: 1 July 1971
Published: 1 July 1972
Hyo Chul Myung