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Numerous important lattices ($D_4,E_8$, the Coxeter-Todd lattice $K_{12}$, the Barnes-Wall lattice ${\Lambda }_{16}$, the Leech lattice ${\Lambda }_{24}$, as well as the $2$-modular $32$-dimensional lattices found by Quebbemann and Bachoc) possess algebraic structures over various Euclidean rings, e.g. Eisenstein integers or Hurwitz quaternions. One obtains efficient algorithms by performing within this frame the usual reduction procedures, including the well known LLL-algorithm.