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
Partially ordered ring a ring "A" to the set of its non-negative elements is one-to-one; that is, the compatible partial order uniquely determines the set of non-negative elements, and a set of elements uniquely determines the compatible partial order if one exists. If "S" is a subset of a ring "A", and: then the relation formula_1 where formula_2 iff formula_24 defines a compatible partial order on "A" ("ie." formula_8 is a partially ordered ring). In any l-ring, the "absolute value" formula_26 of an element "x" can be defined to be formula_27, where formula_28 denotes the maximal element. For any "x" and "y", holds.