skew field: meaning, definition, pronunciation and examples
Very Low (Technical)Formal, Academic, Technical
Quick answer
What does “skew field” mean?
A non-commutative division algebra in mathematics.
Audio
Pronunciation
Definition
Meaning and Definition
A non-commutative division algebra in mathematics
An algebraic structure in which multiplication is not necessarily commutative, but every non-zero element has a multiplicative inverse
Dialectal Variation
British vs American Usage
Differences
No significant regional differences in usage or meaning. Both British and American mathematicians use the term identically.
Connotations
None beyond mathematical technicality
Frequency
Extremely rare outside mathematics; identical low frequency in both varieties
Grammar
How to Use “skew field” in a Sentence
skew field over [ground field]skew field of [specific type]skew field with [property]Vocabulary
Collocations
Examples
Examples of “skew field” in a Sentence
verb
British English
- No verb usage
American English
- No verb usage
adverb
British English
- No adverbial usage
American English
- No adverbial usage
adjective
British English
- No adjectival usage
American English
- No adjectival usage
Usage
Meaning in Context
Business
Not used
Academic
Used exclusively in advanced mathematics, particularly abstract algebra and ring theory
Everyday
Not used
Technical
Specific to mathematical research and advanced textbooks
Vocabulary
Synonyms of “skew field”
Vocabulary
Antonyms of “skew field”
Watch out
Common Mistakes When Using “skew field”
- Confusing with 'field' in general algebra
- Using in non-mathematical contexts
- Assuming it relates to statistics or data 'skewness'
FAQ
Frequently Asked Questions
A field has commutative multiplication, while a skew field (division ring) allows non-commutative multiplication.
No, this is an exclusively mathematical term used in abstract algebra and related fields.
'Division ring' more clearly indicates the structure's properties without the potentially confusing 'skew' modifier.
Quaternions, a type of skew field, are used in computer graphics, robotics, and aerospace for 3D rotations.
A non-commutative division algebra in mathematics.
Skew field is usually formal, academic, technical in register.
Skew field: in British English it is pronounced /skjuː fiːld/, and in American English it is pronounced /skju fild/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None”
Learning
Memory Aids
Mnemonic
Think 'skew' as 'askew' or 'off-center' - it's a field where multiplication doesn't follow the straight (commutative) path
Conceptual Metaphor
A playing field where the rules of movement are asymmetrical
Practice
Quiz
Which of these is a well-known example of a skew field?