noun
Meaning 1
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.
Definition source: English Wiktionary via Wiktextract
Qualifier: ring theory
Topics: algebra, mathematics, sciences
Examples
- 2008, Jan Hendrik Bruinier, Hilbert Modular Forms and Their Applications, Jan Hendrik Bruinier, Gerard van der Geer, Günter Harder, Don Zagier (editors), The 1-2-3 of Modular Forms: Lectures at a Summer School, Springer, page 106, A fractional ideal of F is a finitely generated O_F-submodule of F. Fractional ideals form a group together with the ideal multiplication. The neutral element is O_F and the inverse of a fractional ideal a⊂F is a−1=x∈F;xa⊂O_F. [...] Two fractional ideals a,b are called equivalent, if there is a r∈F such that a=rb.
Meaning relationships
Synonyms: none provided
Antonyms: none provided