A categorical genealogy for the congruence distributive property.
It is shown that in a finitely decidable equational class, the solvable radical of any finite subdirectly irreducible member is comparable to all congruences of the irreducible if the type of the monolith is 2. In the type 1 case we establish that the centralizer of the monolith is strongly solvable.
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
Usando la teoria del commutatore in algebra universale, si dimostra che una larga classe di algebre di incidenza sono polinomialmente equivalenti a moduli su anelli con divisione.