caa a22 4500 445345330 CHVBK 20180317142827.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00233-011-9311-0 doi (NATIONALLICENCE)springer-10.1007/s00233-011-9311-0 On regularity of sup-preserving maps: generalizing Zareckiĭ's theorem [Elektronische Daten] [Ulrich Höhle, Tomasz Kubiak] A sup-preserving map f between complete lattices L and M is regular if there exists a sup-preserving map g from M to L such that fgf=f. In the class of completely distributive lattices, this paper demonstrates a necessary and sufficient condition for f to be regular. When L=M is a power set, our theorem reduces to the well known Zareckiĭ's theorem which characterizes regular elements in the semigroup of all binary relations on a set. Another application of our result is a generalization of Zareckiĭ's theorem for quantale-valued relations. The Author(s), 2011 Sup-preserving map nationallicence Regular map nationallicence Complete distributivity nationallicence Regular relation nationallicence Quantale nationallicence Quantale-valued relation nationallicence Höhle Ulrich Fachbereich C Mathematik und Naturwissenschaften, Bergische Universität, Gaußstraße 20, 42097, Wuppertal, Germany aut Kubiak Tomasz Wydział Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, Umultowska 87, 61-614, Poznań, Poland aut Semigroup Forum Springer-Verlag 83/2(2011-10-01), 313-319 0037-1912 83:2<313 2011 83 233 https://doi.org/10.1007/s00233-011-9311-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9311-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Höhle Ulrich Fachbereich C Mathematik und Naturwissenschaften, Bergische Universität, Gaußstraße 20, 42097, Wuppertal, Germany aut NATIONALLICENCE 700 1- Kubiak Tomasz Wydział Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, Umultowska 87, 61-614, Poznań, Poland aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/2(2011-10-01), 313-319 0037-1912 83:2<313 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer