# Z

## 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.

## Zonotope

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.

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An On-line Dictionary of Combinatorics