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
Near-ring Near-ring In mathematics, a near-ring (also near ring or nearring) is an algebraic structure similar to a ring but satisfying fewer axioms. Near-rings arise naturally from functions on groups. A set "N" together with two binary operations + (called "addition") and ⋅ (called "multiplication") is called a (right) "near-ring" if: Similarly, it is possible to define a "left near-ring" by replacing the right distributive law A3 by the corresponding left distributive law. Both right and left near-rings occur in the literature; for instance, the book of Pilz uses right near-rings, while the book of Clay uses left near-rings. An immediate