ITBM-Constructive Completions of Algebras

We introduce the notion of ITBM-constructive algebra, which is a generalization of the notion of constructive algebra,and study completions of such algebras.We obtain some criterion for the existence of completions for metrized algebrasand prove that each ITBM-constructive metrized algebrawhich has completion can be naturally extended to the ITBM-constructivecompletion. Using these results, we establish the existence ofITBM-constructive presentations for some particular algebras.