ON THE GROENEWALD-HEYMAN STRONGLY PRIME RADICAL

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Abstract
Strongly prime rings were introduced by Handelman and Lawrence [6], and in a recent paper [5] Groenewald and Heyman investigated the upper radical determined by the class of all strongly prime rings. In this paper we continue this investigation. Section 1 provides some alternative characterizations of the radical and in section 2 we discuss general properties of the radical and compare it with other well-known radicals. Finally, combinatorial results on polynomial identities are presented which, combined with our results in section 2. yield some new comnutativity theorems. All rings considered are associative, but do not necessarily have an identity. As usual, I Δ A means that I is an ideal of the ring A. The notation and (xl,x2,…) will stand for the subring and ideal, respectively, generated by the elements x1,x2,…. The rignt annihirator of a subset S of a ring A will be denoted by annA(S). This work was supported in part by NSERC grants A-8775 and A-8789. and was completed while the first and third authors were visiting Dalhousie University. These authors would like to thank the Department of Mathematics, Statistics and Computing Science at Oalhousie University for its generous hospitality.

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