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algebra over a field

algebra over a field noun: an algebra over a ring such that the ring is in fact a field. As a module over a field, such an algebra is in particular a vector space.

Noun

algebra over a field (plural algebras over a field)

  1. An algebra over a ring such that the ring is in fact a field. As a module over a field, such an algebra is in particular a vector space.
    Synonyms:
    algebra, k-algebra

Synonyms of algebra over a field

Forms of algebra over a field

pluralalgebras over a field

Questions about algebra over a field

What does algebra over a field mean?
Algebra over a field means an algebra over a ring such that the ring is in fact a field. As a module over a field, such an algebra is in particular a vector space.
What part of speech is algebra over a field?
Algebra over a field is a noun.
What is the plural of algebra over a field?
The plural of algebra over a field is algebras over a field.

Words near algebra over a field in the dictionary

  1. algate
  2. algates
  3. algazel
  4. algazels
  5. algebra
  6. algebra over a field
  7. algebra over a ring
  8. algebraic
  9. algebraic analysis
  10. algebraic closure
  11. algebraic closure operator

Source and license

Adapted from Wiktionary: algebra over a field (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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