(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.

plural of ideal gas

(mathematics) A certain kind of subset of a partially ordered set.

(algebra, commutative algebra, ring theory) An ideal I within a ring R that is its own radical (i.e., for any r ∈ R, if rⁿ ∈ I for some positive integer n, then r ∈ I).