factor ideal

Noun

 * 1)  For given ring R, any ideal I such that Q = R / I, the set of cosets of elements of I in R, is a ring (the quotient ring of I in R).
 * 2) * 1965 [Prentice-Hall], Seth Warner, Modern Algebra, 1990, Dover, page 651,
 * Consequently, we may speak of the sequence of invariant factor ideals of a finitely generated unitary module over a principal ideal domain A.
 * 1) * 1985 [W. H. Freeman and Company], Nathan Jacobson, Basic Algebra I, 2nd Edition, Dover, 2009, page 193,
 * We shall now call the sequence of order ideals, ann z1, ann z2, ..., whose uniqueness has just been proved, the invariant factor ideals of the module M.