simple algebra
nounDefinitions
An algebra that contains no nontrivial proper (two-sided) ideals and whose multiplication…
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).
- 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.
The neighborhood
Vish — recursive loop
No curated loop yet for simple algebra. Loops are being traced one word at a time while the ingestion pipeline matures.
sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA