💡 Words with a Similar Meaning to "Factor ideal"
Found via reverse dictionary — words that share a conceptual meaning.
| Word | Definition |
|---|---|
| quotient ringnoun | (algebra, ring theory) For a given ring R and ideal I contained in R, another ring, denoted R / I, whose elements are the cosets of I in R. |
| fractional idealnoun | (algebra, ring theory) 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. |
| primary idealnoun | (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. |
| radical idealnoun | (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). |
| prime idealnoun | In a commutative ring, a (two-sided) ideal I such that for arbitrary ring elements a and b, ab∈I⟹a∈I or b∈I. |
| factor ringnoun | (algebra, ring theory) A quotient ring. |
| prime ringnoun | (algebra, ring theory) Any nonzero ring R such that for any two (two-sided) ideals P and Q in R, the product PQ = 0 (the zero ideal) if and only if P = 0 or Q = 0. |
| radical | Favoring fundamental change, or change at the root cause of a matter. |
| principal ideal ringnoun | (algebra, ring theory) A commutative ring in which every ideal is a principal ideal. |
| unique factorization ringnoun | (algebra, ring theory) A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes. |
| principal idealnoun | (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. |
| idealizernoun | A person who idealizes. |
| idealnoun | A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. |
| local ringnoun | (algebra) A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal. |
| localizationnoun | (software engineering) The act, process, or result of making a product suitable for use in a particular country or region. |
| maximal idealnoun | (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). |
| right idealnoun | (algebra) A subset of a ring which is closed under right-multiplication by any element of the ring. |
| ideal numbernoun | (number theory) An algebraic integer that represents an ideal in the ring of integers of a number field. |
| integral domainnoun | (algebra, ring theory) Any nonzero commutative ring in which the product of nonzero elements is nonzero. |
| total ring of fractionsnoun | (algebra) A ring of fractions of a given ring, such that the set of allowed denominators contains all of the non-zero divisors of the given ring. |
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