TY - JOUR
T1 - Hereditary Torsion Theories for Graphs
AU - Veldsman, S.
N1 - Publisher Copyright:
© 2021, Akadémiai Kiadó, Budapest, Hungary.
PY - 2021/4
Y1 - 2021/4
N2 - Using congruences, a Hoehnke radical can be defined for graphs in the same way as for universal algebras. This leads in a natural way to the connectednesses and disconnectednesses (= radical and semisimple classes) of graphs. It thus makes sense to talk about ideal-hereditary Hoehnke radicals for graphs (= hereditary torsion theories). All such radicals for the category of undirected graphs which allow loops are explicitly determined. Moreover, in contrast to what is the case for the well-known algebraic categories, it is shown here that such radicals for graphs need not be Kurosh–Amitsur radicals.
AB - Using congruences, a Hoehnke radical can be defined for graphs in the same way as for universal algebras. This leads in a natural way to the connectednesses and disconnectednesses (= radical and semisimple classes) of graphs. It thus makes sense to talk about ideal-hereditary Hoehnke radicals for graphs (= hereditary torsion theories). All such radicals for the category of undirected graphs which allow loops are explicitly determined. Moreover, in contrast to what is the case for the well-known algebraic categories, it is shown here that such radicals for graphs need not be Kurosh–Amitsur radicals.
KW - Hoehnke radical
KW - Kurosh–Amitsur radical
KW - connectedness and disconnectedness of graphs
KW - graph congruence
KW - ideal-hereditary radical
KW - torsion theory
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U2 - 10.1007/s10474-021-01134-w
DO - 10.1007/s10474-021-01134-w
M3 - Article
AN - SCOPUS:85100842118
SN - 0236-5294
VL - 163
SP - 363
EP - 378
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
IS - 2
ER -