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fractional ideal

noun

Definitions

  1. Given an integral domain R and its field of fractions K = Frac(R), an R-submodule I of K…

    Given an integral domain R and its field of fractions K = Frac(R), an R-submodule I of K such that for some nonzero r∈R, rI ⊆ R.

    • Products of fractional ideals are again fractional ideals, since if A#92;alpha#92;subseteqR and B#92;beta#92;subseteqR, then (AB)(#92;alpha#92;beta)#92;subseteqR.
    • Theorem 5 The non-zero fractional ideals of a Dedekind domain form a multiplicative group.

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA