Distributive groupoids and symmetry-by-mediality (Q801421)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Distributive groupoids and symmetry-by-mediality |
scientific article; zbMATH DE number 3879170
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distributive groupoids and symmetry-by-mediality |
scientific article; zbMATH DE number 3879170 |
Statements
Distributive groupoids and symmetry-by-mediality (English)
0 references
1984
0 references
It is proved that every distributive idempotent groupoid \(G\) is symmetric-by-medial, i.e. there exists a congruence \(\rho\) of \(G\) such that \(G/\rho\) is symmetric and every block of \(\rho\) is a medial subgroupoid of \(G\). This result has several important consequences. One of them: every free distributive groupoid is cancellative.
0 references
distributive idempotent groupoids
0 references
congruences
0 references
medial subgroupoids
0 references
free distributive groupoids
0 references
