Ecclesiastical ring gold, stone-set ring. Roman Catholic bishops traditionally have their episcopal ring set with an amethyst. Aside from the rings a bishop purchases or is given by others, his rings belong to the Church; he will have inherited the previous bishop's ring collection, which is held in trust. While all hierarchs are accorded the honor of being buried wearing a ring, all rings belonging to the Church will be returned to the Church upon the retirement or death of any hierarch. In a Decree of Pope Boniface IV (A.D. 610) it describes monks raised to the episcopal dignity as "anulo pontificali
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