2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192588We investigate a Lie algebra-type $ κ$-deformed Minkowski space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $ κ$-Minkowski space. The coproduct and the star product corresponding to each of them are found. Utilizing the properties of the {\em{natural}} realization, we construct a scalar field theory on $ κ$-deformed Minkowski space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski space.23 pages, revtex4, no figures, typos corrected, references added; in v3 few references and some comments regarding kappa-Poincare symmetry are included; to appear in EPJCHigh Energy Physics - Theorytext