It is known that the ideals of a Leavitt path algebra LK (E) generated by Pl(E),
by Pc(E) or by Pec(E) are invariant under isomorphism. Though the ideal generated by
Pb∞ (E) is not invariant we find its “natural” replacement (which is indeed invariant): the
one generated by the vertices of Pb∞
p (vertices with pure infinite bifurcations). We also
give some procedures to construct invariant ideals from previous known invariant ideals.
One of these procedures involves topology, so we introduce the DCC topology and relate
it to annihilators in the algebraic counterpart of the work. To be more explicit: if H is a
hereditary saturated subset of vertices providing an invariant ideal, its exterior ext(H) in
the DCC topology of E0 generates a new invariant ideal. The other constructor of invariant
ideals is more categorical in nature. Some hereditary sets can be seen as functors from graphs
to sets (for instance Pl, etc). Thus a second method emerges from the possibility of applying
the induced functor to the quotient graph. The easiest example is the known socle chain
Soc(1)( ) ⊆ Soc(2)( ) ⊆ · · · all of which are proved to be invariant. We generalize this idea to
any hereditary and saturated invariant functor. Finally we investigate a kind of composition
of hereditary and saturated functors which is associative
