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
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