Letmbe a positive cardinal. We denote by Pr(m) (resp.Pt(m)) the class of all ringsRfor whichmis the least cardinal such that all nonzero elements ofRpossess right (resp. left) insulators of cardinality less than m + 1. We also setPr(m) = Un#x2264; m Pr(n). The classes Pr(m),m0, partition the class of all prime rings. Various descriptions of these classes are obtained. In particular ifmis regular thenPr(m) contains just those ringsRsuch thatt(R) = 0 for all proper torsion preradicalston Mod -Rwhose torsion classes are closed under direct products of fewer than m modules. Examples are provided which show thatPr(m) is non-empty for all m 0 and which partially answer the question: for which cardinalsm,nisPr(m) #x2229;Pt(n) nonempty?
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