Zero Divisor

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.

Zorn's Lemma

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.

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

An On-line Dictionary of Combinatorics