# finite algebra in a sentence

- There also exists a single
*finite algebra* generating a ( non-congruence-distributive ) variety with arbitrarily large subdirect irreducibles. - It follows that the theory of varieties is of limited use in the study of
*finite algebras*, where one must often apply techniques particular to the finite case. - Not every author assumes that all algebras on a pseudovariety are finite; if this is the case, one sometimes talks of a "'variety of
*finite algebras* " '. - Thus when generalizing
*finite algebras* ( of any kind, not just Boolean ) to infinite ones, " discrete " and " compact " part company, and one must choose which one to retain. - By J髇sson's lemma, subdirectly irreducible algebras of a congruence-distributive variety generated by a finite set of
*finite algebras* are no larger than the generating algebras, since the quotients and subalgebras of an algebra " A " are never larger than " A " itself. - It's difficult to find
*finite algebra* in a sentence. - Given any class " C " of similar algebras, J髇sson's lemma states that if the variety HSP ( " C " ) generated by " C " is congruence-distributive, its subdirect irreducibles are in HSP U ( " C " ), that is, they are quotients of subalgebras of ultraproducts of members of " C " . ( If " C " is a finite set of
*finite algebras*, the ultraproduct operation is redundant .)