skew field: meaning, definition, pronunciation and examples

Very Low (Technical)
UK/skjuː fiːld/US/skju fild/

Formal, Academic, Technical

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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

strong
non-commutative skew fieldfinite skew fielddivision ring and skew field
medium
example of a skew fieldstructure of a skew fieldelements of a skew field
weak
mathematical skew fieldalgebraic skew fieldskew field theory

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”

Strong

non-commutative division algebra

Weak

non-commutative field (colloquial)

Vocabulary

Antonyms of “skew field”

commutative fieldfield (in the strict algebraic sense)

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

Fill in the gap
A is an algebraic structure where multiplication is not necessarily commutative but every non-zero element has an inverse.
Multiple Choice

Which of these is a well-known example of a skew field?

skew field: meaning, definition, pronunciation and examples | Lingvocore