Phrase guide

simple algebra

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

An algebra that contains no nontrivial proper (two-sided) ideals and whose multiplication operation is not zero (i.e., there exist a and b such that ab ≠ 0).

Definition source: English Wiktionary via Wiktextract

Topics: algebra, mathematics, sciences

Examples

  • 1945 [McGraw-Hill], E. T. Bell, 2nd Edition, 1992, Dover, The Development of Mathematics, page 252, A semi-simple algebra over F is either simple or the direct sum of simple algebras over F.
  • 1989 [W. H Freeman & Company], Nathan Jacobson, Basic Algebra II, 2nd Edition, 2009, Dover, page 215, If A is a finite dimensional simple algebra over F, then A≅M_n(Δ) where Δ is a finite dimensional division algebra over Δ.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

2 source translations are retained for this English entry.

  • Italian: algebra semplice — algebra that contains no nontrivial proper ideals and whose multiplication operation is not zero
  • Polish: algebra prosta — algebra that contains no nontrivial proper ideals and whose multiplication operation is not zero