Word.ws English Dictionary

fractional ideal

fractional ideal noun: 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.

Noun

fractional ideal (plural fractional ideals)

  1. (ring theory) 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.1994, I. Martin Isaacs, Algebra: A Graduate Course, American Mathematical Society, page 476
    • Theorem 5 The non-zero fractional ideals of a Dedekind domain form a multiplicative group.2001, H. P. F. Swinnerton-Dyer, A Brief Guide to Algebraic Number Theory, Cambridge University Press, page 10
    Synonyms:
    R-submodule of Frac(R) such that for some nonzero r∈R, rI ⊆ R

fractional ideal meaning in Tamil

fractional ideal in Tamil

பின்னச் சீர்மம்

Synonyms of fractional ideal

  • R-submodule of Frac(R) such that for some nonzero r∈R
  • rI ⊆ R

Forms of fractional ideal

pluralfractional ideals

Questions about fractional ideal

What does fractional ideal mean?
Fractional ideal means 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.
What is fractional ideal in Tamil?
Fractional ideal in Tamil is பின்னச் சீர்மம். See Fractional ideal meaning in Tamil.
What part of speech is fractional ideal?
Fractional ideal is a noun.
What is the plural of fractional ideal?
The plural of fractional ideal is fractional ideals.

Words near fractional ideal in the dictionary

  1. fractional crystallizations
  2. fractional distillation
  3. fractional distillations
  4. fractional freezing
  5. fractional freezings
  6. fractional ideal
  7. fractional ideals
  8. fractional number
  9. fractional numbers
  10. fractional reserve banking
  11. fractional rig

Source and license

Adapted from Wiktionary: fractional ideal (page history and authors); fractional ideal (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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