Faculty Publications

A Generalization Of The Prime Radical In N On Associ At Ive Rings

Document Type

Article

Journal/Book/Conference Title

Pacific Journal of Mathematics

Volume

42

Issue

1

First Page

187

Last Page

193

Abstract

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/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 ^-operation and the function /. We also extend the results for the Jordan case to weakly Inadmissible rings which include the generalized standard rings and therefore alternative and standard rings as well as Jordan rings. © 1972, Pacific Journal of Mathematics.

Department

Department of Mathematics

Original Publication Date

1-1-1972

DOI of published version

10.2140/pjm.1972.42.187

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