Abstract: In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field R_1, R₂ be K-algebras, we also obtain a sufficient condition for lgldim (R₁ R₂,)≥lgldim R₁+lgldimR₂, and wgldim (R₁ ) ≥wgldimR₁ +wgldimR₂ .

Key words: inverse limit, tensor product, meta-projective modules, meta-injective modules