Search Results for ""

The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F. For example, the field of ...

If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.

A finite division algebra is a field.

The portion of number theory concerned with expressing an integer as a sum of integers from some given set.

Axiomatic set theory is a version of set theory in which axioms are taken as uninterpreted rather than as formalizations of pre-existing truths.

A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

Combinatorial game theory is the theory of two-player games of perfect knowledge such as go, chess, or checkers.

The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel set theory is replaced by 6'. Selection axiom (or "axiom of subsets"): for any set-theoretic formula A(u), ...