Subdirect Irreducibles

Some articles on subdirect, irreducible, subdirect irreducible, subdirect irreducibles:

Subdirectly Irreducible Algebra - Properties
... The subdirect representation theorem of universal algebra states that every algebra is subdirectly representable by its subdirectly irreducible quotients ... An equivalent definition of "subdirect irreducible" therefore is any algebra A that is not subdirectly representable by those of its quotients not ... closed under homomorphisms, subalgebras, and direct products, is determined by its subdirectly irreducible members, since every algebra A in the variety can be constructed as a ...
Subdirectly Irreducible Algebra - Applications
... A necessary and sufficient condition for a Heyting algebra to be subdirectly irreducible is for there to be a greatest element strictly below 1 ... Hence every finite chain of two or more elements as a Heyting algebra is subdirectly irreducible ... By Jónsson's Lemma the subdirect irreducibles of the variety generated by a class of subdirect irreducibles are no larger than the generating subdirect irreducibles, since the ...