2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161732As an attempt to understand motives over $k[x]/(x^m)$, we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. Rülling on 0-dimensional cycles. We give an explicit construction of regulator maps on the groups of 1-cycles with an aid of the residue theory of A. Parshin and V. Lomadze.17 pages; 2 figures; v2) introduction revised; typos corrected; some notations changed to be more coherent; some remarks corrected; v3) further typos corrected. compactified. a version of this paper to appear in Amer. J. MathAlgebraic GeometryK-Theory and Homology14C15; 19D55text