fractional ideal

(redirected from Integral ideal)

fractional ideal

[¦frak·shən·əl i′dēl]
(mathematics)
A submodule of the quotient field of an integral domain.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Mentioned in ?
References in periodicals archive ?
Let g =[F : Q], D(F) be the discriminant of F/Q, p be a prime such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], r a positive integer, [[member of].sub.1], [[member of].sub.2],..., [[member of].sub.r] [member of] {0 , [+ or -]1} such that [[member of].sub.i] [not equal to] 0 for some i, [[chi].sub.1], [[chi].sub.2], ..., [[chi].sub.r] be quadratic Hecke characters of F whose conductor is integral ideal [N.sub.1], [N.sub.2],..., [N.sub.r] respectively.
the pair (a , b) runs the all integral ideals relatively prime to 2[O.sub.F] such that [(ab).sup.2]|2[xi][O.sub.F], [mu] is the Mobius function, [Q.sub.F([square root of -2[xi])] [member of]{[+ or -]1} is the Hasse index of F([square root of 2[xi]]), and [w.sub.F([square root of -2[xi])] is the number of roots of unity in F([square root of -2[xi]]).