plural of factor ideal

plural of fractional ideal

(algebra, ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure).

(algebra, ring theory) Given a commutative ring R, any ideal I such that for any a,b ∈ R, if ab ∈ I then either b ∈ I or aⁿ ∈ I for some integer n > 0.

plural of primary ideal

plural of beau-ideal

Alternative form of beau idéal

(algebra) An ideal I in an algebraic object R (which could be a ring, algebra, semigroup or lattice) that is generated by a given single element a ∈ R; the smallest ideal that contains a.

(algebra) A subring which is closed under right-multiplication by any element of the ring.

(algebra) A subring which is closed under left-multiplication by any element of the ring.