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An ordering for the Cartesian product × of any two sets A and B with order relations <A and <B, respectively, such that if (a_1,b_1) and (a_2,b_2) both belong to A×B, then ...

Let K be a number field of extension degree d over Q. Then an order O of K is a subring of the ring of integers of K with d generators over Z, including 1. The ring of ...

Every totally ordered set (A,<=) is associated with a so-called order type. Two sets A and B are said to have the same order type iff they are order isomorphic (Ciesielski ...

A partially ordered set P is a circle order if it is isomorphic to a set of disks ordered by containment.

A well ordered set of monomials which also satisfies the condition "u<v implies uw<vw" for all monomials u, v, and w. Examples of monomial orders are the lexicographic order ...

A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

The infimum of all number a for which |f(z)|<=exp(|z|^a) holds for all |z|>r and f an entire function, is called the order of f, denoted lambda=lambda(f) (Krantz 1999, p. ...

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...