caa a22 4500 469026898 CHVBK 20180323132732.0 cr unu---uuuuu 170328e19920901xx s 000 0 eng 10.1007/BF01212436 doi (NATIONALLICENCE)springer-10.1007/BF01212436 Pap Endre Institute of Mathematics, Novi Sad, Yugoslavia aut Intrinsic metrics preserving maps on Abelian lattice-ordered groups [Elektronische Daten] [Endre Pap] Swamy studied the natural "metric” ¦x−y¦ on Abelian lattice-ordered groupsG, and he proved that the stable isometries which preserve this metric have to be automorphisms ofG. Holland proved that the only intrinsic metrics on lattice-ordered groups, i.e., invariant and symmetric metrics, are the multiples n¦x −y¦ for some integern. We show that iff is an arbitrary surjection from an Abelian lattice-ordered groupG 1 onto an Archimedean Abelian lattice-ordered groupG 2 such that f(0)]0 and, for some non-zero intrinsic metricsD andd, D(f(x),f(y)) depends functionally on d(x,y), thenf is a homomorphism of G1 onto G2. Birkhäuser Verlag, 1992 algebra universalis Birkhäuser-Verlag 29/3(1992-09-01), 338-345 0002-5240 29:3<338 1992 29 12 https://doi.org/10.1007/BF01212436 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01212436 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pap Endre Institute of Mathematics, Novi Sad, Yugoslavia aut NATIONALLICENCE 773 0- algebra universalis Birkhäuser-Verlag 29/3(1992-09-01), 338-345 0002-5240 29:3<338 1992 29 12 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer