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
Graded ring The associativity is not important (in fact not used at all) in the definition of a graded ring; hence, the notion applies to a non-associative algebra as well; e.g., one can consider a graded Lie algebra. Let be a graded ring. Elements of any factor formula_4 of the decomposition are called homogeneous elements of degree "n". Every element "a" of "R" may be uniquely written as a sum "a" = "a" + "a" + ... + "a" with all "a" homogeneous elements of distinct "R". These "a" are called the homogeneous components of "a". Some basic properties are: An ideal