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The class of s-rings includes as a proper subset the classes of associative, alternative, Lie, Jordan, and standard rings. It is shown that in any s-ring R the prime radical of R coincides with the Baer lower radical of R. Relationships between the prime radical and certain other radicals are also given.doi:10.2307/2038215 fatcat:l3kjmtfqtrekrelsio3qkg5f4q