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Classifications of subdirectly irreducible involution rings via some properties of trace elements are given. As an application, von Neumann regular involution rings with central idempotent norm elements are described. The structure of certain involution rings in which the norms are multiplicatively generated by nilpotents is also determined.doi:10.18514/mmn.2009.206 fatcat:5fj7iayxo5cjlbm3b5vym5eaae