💡 Words with a Similar Meaning to "Prime ring"
Found via reverse dictionary — words that share a conceptual meaning.
| Word | Definition |
|---|---|
| simple ringnoun | (algebra, ring theory) A ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself). |
| principal ideal ringnoun | (algebra, ring theory) A commutative ring in which every ideal is a principal ideal. |
| 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. |
| product ringnoun | (mathematics, ring theory) A ring that is the direct product of rings. |
| division ringnoun | (algebra) A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = 1. |
| 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. |
| reduced ringnoun | (algebra, ring theory) A ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0. |
| 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. |
| factor idealnoun | (algebra, ring theory) 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). |
| factor ringnoun | (algebra, ring theory) A quotient ring. |
| 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. |
| idealnoun | A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. |
| ordered ringnoun | (algebra, order theory, ring theory) A ring, R, equipped with a total order, ≤, such that for arbitrary a, b, c ∈ R, if a ≤ b then a + c ≤ b + c, and if, additionally, 0 ≤ c, then both ca ≤ cb and ac ≤ bc. |
| pseudoradical | Claiming or appearing to be politically radical, but not actually so. |
| integral domainnoun | (algebra, ring theory) Any nonzero commutative ring in which the product of nonzero elements is nonzero. |
| right idealnoun | (algebra) A subset of a ring which is closed under right-multiplication by any element of the ring. |
| primitive polynomialnoun | (algebra, field theory) A polynomial over a given finite field whose roots are primitive elements; especially, the minimal polynomial of a primitive element of said finite field. |
| radical | Favoring fundamental change, or change at the root cause of a matter. |
| minimal idealnoun | (algebra, ring theory) A nonzero (two-sided) ideal that contains no other nonzero two-sided ideal. |
| 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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