💡 Words with a Similar Meaning to "Reduced 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). |
| reduced algebranoun | (algebra, ring theory) An algebra over a reduced ring. |
| 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. |
| zero divisornoun | (algebra, ring theory) A nonzero element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0. |
| 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. |
| domainnoun | A field or sphere of activity, influence or expertise. |
| near-ringnoun | (mathematics) An algebraic structure similar to a ring but satisfying fewer axioms. They arise naturally from functions on groups. |
| factor ringnoun | (algebra, ring theory) A quotient ring. |
| 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. |
| noetherian ringnoun | (algebra, ring theory) A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated). |
| 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. |
| boolean ringnoun | (algebra) A ring whose multiplicative operation is idempotent. |
| semiringnoun | (algebra) An algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. |
| 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. |
| minimal idealnoun | (algebra, ring theory) A nonzero (two-sided) ideal that contains no other nonzero two-sided ideal. |
| zeronoun | The numeric symbol that represents the cardinal number zero. |
| regular elementnoun | (algebra) An element of a ring that is not a zero divisor. |
| idealnoun | A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. |
| radical | Favoring fundamental change, or change at the root cause of a matter. |
| ringoidnoun | (mathematics) A ring-like algebraic structure. |
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