RT Journal Article
T1 Invariant ideals in Leavitt path algebras.
A1 Gil-Canto, Cristóbal
A1 Martín-Barquero, Dolores
A1 Martín-González, Cándido
K1 Álgebra
AB 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 byPb∞ (E) is not invariant we find its “natural” replacement (which is indeed invariant): theone generated by the vertices of Pb∞p (vertices with pure infinite bifurcations). We alsogive some procedures to construct invariant ideals from previous known invariant ideals.One of these procedures involves topology, so we introduce the DCC topology and relateit to annihilators in the algebraic counterpart of the work. To be more explicit: if H is ahereditary saturated subset of vertices providing an invariant ideal, its exterior ext(H) inthe DCC topology of E0 generates a new invariant ideal. The other constructor of invariantideals is more categorical in nature. Some hereditary sets can be seen as functors from graphsto sets (for instance Pl, etc). Thus a second method emerges from the possibility of applyingthe induced functor to the quotient graph. The easiest example is the known socle chainSoc(1)( ) ⊆ Soc(2)( ) ⊆ · · · all of which are proved to be invariant. We generalize this idea toany hereditary and saturated invariant functor. Finally we investigate a kind of compositionof hereditary and saturated functors which is associative
PB Universitat Autònoma de Barcelona, Departament de Matemàtiques. Revista: Publications Matematiques
YR 2020
FD 2020-06-23
LK https://hdl.handle.net/10630/28159
UL https://hdl.handle.net/10630/28159
LA spa
NO The authors are supported by the Junta de Andaluc ́ıa through projects FQM-336 and UMA18-FEDERJA-119 and by the Spanish Ministerio de Ciencia e Innovaci ́on through project PID2019-104236GB-I00/AEI/10.13039/501100011033, all of them with FEDER funds.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026