Definition:Principal

Disambiguation

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Principal may refer to:

• Logic:
  • Principal operator: another name for main connective.

• Order Theory:
  • Principal ideal of a preordered set: an ideal with an upper bound.

• Matrix Algebra:
  • Principal diagonal: another name for main diagonal.

• Complex Analysis:
  • Principal branch: a distinguished branch of a complex multifunction.
    • Principal range: the interval in which the argument lies so that the image lies on the principal branch.
    • Principal argument: the argument of the unique preimage of an element of the principal branch.
  • Principal square root: the principal branch of the $2$nd power of a complex number.

• Number Theory:
  • Principal remainder: another name for what $\mathsf{Pr} \infty \mathsf{fWiki}$ defines as the remainder of an integer division.

• Analytic Number Theory:
  • Principal character: another name for trivial character.

• Ideal Theory:
  • Principal ideal: an ideal of a ring generated by an element of that ring.
  • Principal ideal domain: an integral domain in which every ideal is a principal ideal.

• Filter Theory:
  • Principal ultrafilter: an ultrafilter on $S$ with a cluster point.

• Economics:
  • Principal: a quantity of money that is either borrowed or invested.

Linguistic Note

The word principal is (except in the context of economics) an adjective which means main.

Do not confuse with the word principle, which is a noun.