On rings with prime centers.
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2010 Mathematics Subject Classification: 16R20, 16R50, 16R60, 16N60. We give short proofs, based only on basic properties of the extended centroid of a prime ring, of Martindale’s theorem on prime GPI-rings and (a strengthened version of) Posner’s theorem on prime PI-rings. * Supported by the Slovenian Research Agency (program No. P1-0288).
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