Mathematics::Domain

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Mathematics

• Domain of a function, the set of input values for which the function is defined
• Domain of discourse, the set of entities over which logic variables may range
• Domain (mathematical analysis), an open connected set
• Domain (ring theory), a nontrivial ring without left or right zero divisors
  • Atomic domain, an integral domain in which every non-zero non-unit is a finite product of irreducible elements
  • Bézout domain, an integral domain in which the sum of two principal ideals is again a principal ideal
  • Euclidean domain, an integral domain which allows a suitable generalization of the Euclidean algorithm
  • Dedekind domain, an integral domain in which every nonzero proper ideal factors into a product of prime ideals
  • GCD domain, an integral domain in which every two non-zero elements have a greatest common divisor
  • Integral domain, a non-trivial commutative ring without zero divisors
  • Principal ideal domain, an integral domain in which every ideal is principal
  • Unique factorization domain, an integral domain in which every non-zero element can be written as a product of irreducible elements in essentially a unique way
• Frequency domain, the analysis of mathematical functions with respect to frequency, rather than time
• Fundamental domain, a symmetry group of an object is a part or pattern, as small or irredundant as possible, which determines the whole object based on the symmetry
• Time domain, the analysis of mathematical functions with respect to time
• Domain theory, studying certain kinds of partial ordered sets

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