TURKISH JOURNAL OF MATHEMATICS, cilt.32, sa.3, ss.277-292, 2008 (SCI-Expanded)
Nonlinear semi-discrete equations of the form t(x)(n+ 1) = f(t(n), t(n + 1), t(x)(n)) are studied. An adequate algebraic formulation of the Darboux integrability is discussed and an attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.