noun
Meaning 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).
Definition source: English Wiktionary via Wiktextract
Qualifier: ring theory
Topics: algebra, mathematics, sciences
Examples
- 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.
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided