Phrase Hound found 15 phrases and 4 compound words that contain ideals. The most common are listed below. Open ideals in the live search for definitions, filters, and the full list.
Phrases 15
- prime idealsplural of prime ideal: Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
- factor idealsplural of factor ideal: 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).
- left idealsplural of left ideal: A subset of a ring which is closed under left-multiplication by any element of the ring.
- minimal idealsplural of minimal ideal: A nonzero (two-sided) ideal that contains no other nonzero two-sided ideal.
- primary idealsplural of primary ideal: 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.
- principal idealsplural of principal ideal: 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.
- radical idealsplural of radical ideal: 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).
- right idealsplural of right ideal: A subset of a ring which is closed under right-multiplication by any element of the ring.
- maximal idealsplural of maximal ideal: 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).
- fractional idealsplural of fractional ideal: Given an integral domain R and its field of fractions K = Frac(R), an R-submodule I of K such that for some nonzero r∈R, rI ⊆ R.
- beau-idealsplural of beau-ideal: Ideal excellence, or an imaginary standard of perfection.
- vanishing idealsplural of vanishing ideal: An ideal consisting of all polynomials (belonging to a certain polynomial ring) which zero out within a given algebraic variety.
- two-sided idealsplural of two-sided ideal: A subset of a ring which is both a left ideal and a right ideal. Commonly referred to simply as an ideal, but referred to as two-sided ideal for emphasis.
- Platonic idealsplural of Platonic ideal: A perfect, idealized notion of something, taken to exist beyond the physical world.
- Frink idealsplural of Frink ideal: A certain kind of subset of a partially ordered set.
Compound words 4
- hyperidealsplural of hyperideal: An ideal of a semihypergroup.
- counteridealsplural of counterideal: An opposing ideal.
- pseudoidealsplural of pseudoideal: The set of all lower bounds of the set of all upper bounds of a subset of a partially ordered set
- subidealsplural of subideal