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We study decomposition of the nonabelian gauge field into the Abelian component created by Abelian monopoles and the modified nonabelian components with monopoles removed after fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics. We compute the static potential V ® for the original gauge field and for its components V_mon and V_mod at two values of the lattice spacing. We confirm that with optimal gauge fixing the sum V_mon + V_mod deviates substantially from V®. We show that this decomposition of the static potential is satisfied with good precision at all distances when we use another set of Gribov copies.

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