reduced ring
reduced ring noun: a ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0.
Noun
reduced ring (plural reduced rings)
- A ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0.
- We do this for reduced rings in Corollary 10, and for rings with nonzero nilpotents in Corollary 15.1997, Thomas G. Lucas, “Characterizing When R(X) is Completely Integrally Closed”, in Daniel Anderson, editor, Factorization in Integral Domains, Marcel Dekker, page 401
- Extending the notion of a reduced ring, we call a right module M over a ring R a reduced module if, for any m#92;inM and a#92;inR, ma#61;0 implies mR#92;capMa#61;0. Various results of reduced rings are extended to reduced modules.2004, Tsiu-Kwen Lee, Yiqiang Zhou, “Reduced Modules”, in Alberto Facchini, Evan Houston, Luigi Salce, editors, Rings, Modules, Algebras, and Abelian Groups, Marcel Dekker, page 365
Forms of reduced ring
| plural | reduced rings |
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Questions about reduced ring
- What does reduced ring mean?
- Reduced ring means a ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0.
- What part of speech is reduced ring?
- Reduced ring is a noun.
- What is the plural of reduced ring?
- The plural of reduced ring is reduced rings.
Words near reduced ring in the dictionary
Source and license
Adapted from Wiktionary: reduced ring (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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