💡 Words with a Similar Meaning to "Division ring"
Found via reverse dictionary — words that share a conceptual meaning.
| Word | Definition |
|---|---|
| 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. |
| boolean ringnoun | (algebra) A ring whose multiplicative operation is idempotent. |
| 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 ringnoun | (algebra, ring theory) A ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0. |
| domainnoun | A field or sphere of activity, influence or expertise. |
| 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. |
| 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. |
| 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. |
| 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. |
| semiringnoun | (algebra) An algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. |
| 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. |
| skew fieldnoun | (algebra, dated) A ring in which every nonzero element has a multiplicative inverse; division ring |
| integral domainnoun | (algebra, ring theory) Any nonzero commutative ring in which the product of nonzero elements is nonzero. |
| division algebranoun | (algebra) An algebra over a field such that every non-zero element of it has a multiplicative inverse. (It is not required to have a unity element.) |
| product ringnoun | (mathematics, ring theory) A ring that is the direct product of rings. |
| commutative ringnoun | (algebra, ring theory) A ring whose multiplicative operation is commutative. |
| ring of fractionsnoun | (algebra) A ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0. |
| zeronoun | The numeric symbol that represents the cardinal number zero. |
| valuation ringnoun | (algebra) An integral domain D such that for every element x of its field of fractions F, at least one of x or x⁻¹ belongs to D. |
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