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
Ring (mathematics) and so is a polynomial ring. To give an example, let "S" be the ring of all functions from "R" to itself; the addition and the multiplication are those of functions. Let "x" be the identity function. Each "r" in "R" defines a constant function, giving rise to the homomorphism formula_133. The universal property says that this map extends uniquely to ("t" maps to "x") where formula_135 is the polynomial function defined by "f". The resulting map is injective if and only if "R" is infinite. Given a non-constant monic polynomial "f" in formula_111, there exists a ring "S" containing