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A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

The order of a finite field is the number of elements it contains.

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

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 ...

A totally ordered set (A,<=) is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element (Ciesielski 1997, p. 38; Moore 1982, ...

A rooted tree in which the order of the subtrees is significant. There is a one-to-one correspondence between ordered forests with n nodes and binary trees with n nodes.

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...

A prime field is a finite field GF(p) for p is prime.

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...