General algebraic systems Products and constructions Concept
Directly indecomposable algebra
Summary
A directly indecomposable algebra is a nontrivial algebra that is not isomorphic to a direct product of two nontrivial algebras. Every finite algebra is a direct product of finitely many directly indecomposable ones. The notion is weaker than subdirect irreducibility, which forbids also the more flexible subdirect decompositions.
Further reading
About this page
| Tag | 6B1PSZ42MC |
|---|---|
| URI | m2://6B1PSZ42MC |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B25, 08A05 |
| Changed | 2 November 2026 |
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