Abstract
A ring satisfies J2 = J for all ideals J if and only if all of its homomorphic images are semiprime; we call such rings ‘fully semiprime’. D. Castella's theory of compressibility of regular Baer rings is extended to fully semiprime Baer rings and Baer ∗—rings. Sample application: If a fully semiprime Baer ring is a matrix ring, then its center is self-injective
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