Definition:Residue

Disambiguation

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Residue may refer to:

• Complex Analysis
  • Residue: the coefficient of $\paren {z - z_0}^{-1}$ in the Laurent series of a complex function

• Number Theory
  • Residue: an integer $a$ is a residue of $m$ of order $n$ if and only if $\exists x \in \Z: x^n \equiv a \pmod m$ for $m, n \in \N$ where $a \perp m$.

• Modulo Arithmetic
  • Residue: an integer congruent to $a$ modulo $m$.

• Field Theory
  • Residue Field the quotient ring $R / m$ of a commutative local ring $R$ by its maximal ideal $m$.

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