ABSTRACT
IT is clear that the arithmetic in an arbitrary ring can differ substantially from the well-known arithmetic in the ring of integers. One example is the possible noncommutativity of multiplication. But even in commutative rings unfamiliar phenomena can occur. We will point out these phenomena and then define a class of rings in which they cannot occur. These rings then resemble the integers much more than arbitrary rings which has the consequence that a reasonable theory of divisibility can be established. Let us start by considering special elements that can occur in a ring.
