Ecclesiastical ring the new pope. The pope's ring is not to be confused with the papal seal, which is what the pope uses to seal documents. The Fisherman's Ring is no longer used to seal anything. Except Pope Benedict XVI, who chose to wear his at all times, the ring had not been seen being publicly worn by a pope since the papacy of Pope Pius XII, who refrained from wearing it once his election ceremonies had been concluded. A collection of rings belonging to the popes of the past is exhibited in a glass case in a room within the papal
Noncommutative ring is isomorphic to a product of finitely many "n"-by-"n" matrix rings over division rings "D", for some integers "n", both of which are uniquely determined up to permutation of the index "i". In particular, any simple left or right Artinian ring is isomorphic to an "n"-by-"n" matrix ring over a division ring "D", where both "n" and "D" are uniquely determined. As a direct corollary, the Artin–Wedderburn theorem implies that every simple ring that is finite-dimensional over a division ring (a simple algebra) is a matrix ring. This is Joseph Wedderburn's original result. Emil Artin later generalized it to the