“Geometry of numbers” in a context of algebraic theory of numbers

As noted in circumstantial monograph Geometry of Numbers by P. M. Gruber and C. G. Lekkerkerker, lately there is no considerable contribution to classical theory of calculation and estimates of critical determinants. In this article, in a certain sense, we fill a gap in occurred retardation in developing this theme. We propose a new theoretical-numerical approach with numerous consequences which, in fact, allows to revise all these subjects from another position.