A pair of element x and y of a ring are called zero divisors if neither of them are zero, but their product xy = 0 . A ring without zero divisors is called an integral domain.
The Minkowski sum of line segments.
In set theory, a statement (equivalent to the Axiom of Choice) which asserts that: If S is any non-empty partially ordered set in which every chain has an upper bound, then S has a maximal element.
It should be noted that Zorn's lemma states that under the given conditions S will have a maximal element, it does not say how many maximal elements S may have. A maximal element in a poset is an element such that if any other element is greater than or equal to it, it must in fact be equal to it. A chain in a poset consists of a sub-poset in which every element is comparable.