💡 Words with a Similar Meaning to "Simple ring"
Found via reverse dictionary — words that share a conceptual meaning.
| Word | Definition |
|---|---|
| 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. |
| 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. |
| 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. |
| minimal idealnoun | (algebra, ring theory) A nonzero (two-sided) ideal that contains no other nonzero two-sided ideal. |
| 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. |
| principal ideal ringnoun | (algebra, ring theory) A commutative ring in which every ideal is a principal ideal. |
| domainnoun | A field or sphere of activity, influence or expertise. |
| idealnoun | A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. |
| near-ringnoun | (mathematics) An algebraic structure similar to a ring but satisfying fewer axioms. They arise naturally from functions on groups. |
| 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. |
| simple algebranoun | (algebra) An algebra that contains no nontrivial proper (two-sided) ideals and whose multiplication operation is not zero (i.e., there exist a and b such that ab ≠ 0). |
| semiringnoun | (algebra) An algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. |
| 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). |
| radical | Favoring fundamental change, or change at the root cause of a matter. |
| boolean ringnoun | (algebra) A ring whose multiplicative operation is idempotent. |
| 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. |
| factor ringnoun | (algebra, ring theory) A quotient ring. |
| 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. |
| 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). |
| product ringnoun | (mathematics, ring theory) A ring that is the direct product of rings. |
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