Subdirectly

Some articles on subdirectly:

Subdirectly Irreducible Algebra - Examples
... a Boolean algebra, a Heyting algebra, a lattice, or a semilattice, is subdirectly irreducible ... In fact, a distributive lattice is subdirectly irreducible if and only if it has exactly two elements ... or more elements, as a Heyting algebra, is subdirectly irreducible ...
Subdirect Product - Examples
... Any distributive lattice L is subdirectly representable as a subalgebra of a direct power of the two-element distributive lattice ... with infinity, as a Heyting algebra, is subdirectly representable as a subalgebra of the direct product of the finite linearly ordered Heyting algebras ... The group of integers under addition is subdirectly representable by any (necessarily infinite) family of arbitrarily large finite cyclic groups ...
Subdirectly Irreducible Algebra - Properties
... representation theorem of universal algebra states that every algebra is subdirectly representable by its subdirectly irreducible quotients ... irreducible" therefore is any algebra A that is not subdirectly representable by those of its quotients not isomorphic to A ... closed under homomorphisms, subalgebras, and direct products, is determined by its subdirectly irreducible members, since every algebra A in the variety can be ...