Research any topic before you write.
Find related topics. | Discover entities. | See connections. | Build a topical map.
In abstract algebra, a nonzero ring R is a prime ring if for any two elements a and b of R, arb = 0 for all r in R implies that either a = 0 or b = 0. This definition can be regarded as a simultaneous generalization of both integral domains and simple rings.
Equivalent definitions, Examples & Properties
Explore the main themes, entities and connections around Prime ring. Start with the topic map, then use the sections below for research and deeper semantic analysis.
Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Browse the full topic structure. Each item opens a new analysis centered on that subject.
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
See the strongest relationship patterns around the current topic before diving into the raw triples.
Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
prime ring ideals field nonzero two implies characteristic integral definition domain equivalent ab right left simple rings faithful matrices subring
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Prime ring | is a | integers | 0.90 | text |
| Prime ring | related to Equivalent definitions | This | 0.60 | section |
| Prime ring | related to Examples | Any | 0.60 | section |
| Prime ring | related to Examples | In | 0.60 | section |
| Prime ring | related to Properties | The | 0.60 | section |
These clusters group vocabulary that occurs around closely connected concepts in the source material.
Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.