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Multiplicative distance

In algebraic geometry, is said to be a multiplicative distance function over a field if it satisfies AB is congruent to A'B' iff AB < A'B' iff

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Jun 19, 2026
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In algebraic geometry, μ {\displaystyle \mu } is said to be a multiplicative distance function over a field if it satisfies1

  • μ ( A B ) > 1. {\displaystyle \mu (AB)>1.\,}
  • AB is congruent to A'B' iff μ ( A B ) = μ ( A ′ B ′ ) . {\displaystyle \mu (AB)=\mu (A'B').\,}
  • AB < A'B' iff μ ( A B ) < μ ( A ′ B ′ ) . {\displaystyle \mu (AB)<\mu (A'B').\,}
  • μ ( A B + C D ) = μ ( A B ) μ ( C D ) . {\displaystyle \mu (AB+CD)=\mu (AB)\mu (CD).\,}
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