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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