caa a22 4500 445345381 CHVBK 20180317142827.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00233-011-9330-x doi (NATIONALLICENCE)springer-10.1007/s00233-011-9330-x Using filters to describe congruences and band congruences of semigroups [Elektronische Daten] [Zsófia Juhász, Alexei Vernitski] It is well known that the smallest semilattice congruence can be described via filters. We generalise this result to the smallest left (right) normal band congruences and also to arbitrary semilattice (left normal band, right normal band) congruences, describing them all via filters. To achieve this, we introduce filters relative to arbitrary quasiorders on a semigroup (traditional filters are filters relative to the smallest negative operation-compatible quasiorder). We study congruences which can be described via filters. We show that the lattice of semilattice (left normal band, right normal band) congruences is a homomorphic image of the lattice of negative (right negative, left negative) operation-compatible quasiorders. Springer Science+Business Media, LLC, 2011 Filter nationallicence Semilattice nationallicence Band nationallicence Congruence nationallicence Quasiorder nationallicence Preorder nationallicence Juhász Zsófia Dept. of Math. Sc., University of Essex, CO4 3SQ, Colchester, UK aut Vernitski Alexei Dept. of Math. Sc., University of Essex, CO4 3SQ, Colchester, UK aut Semigroup Forum Springer-Verlag 83/2(2011-10-01), 320-334 0037-1912 83:2<320 2011 83 233 https://doi.org/10.1007/s00233-011-9330-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9330-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Juhász Zsófia Dept. of Math. Sc., University of Essex, CO4 3SQ, Colchester, UK aut NATIONALLICENCE 700 1- Vernitski Alexei Dept. of Math. Sc., University of Essex, CO4 3SQ, Colchester, UK aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/2(2011-10-01), 320-334 0037-1912 83:2<320 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer