Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen–Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, w...

In 1974, the author proved that codimension of ideal (g1,g2,…,gd) generated in group algebra K[Zd] over a field K characteristic 0 by generic Laurent polynomials having same Newton polytope Γ is equal to d!×Volume(Γ). Assuming Newtons simplicial and super-convenient (that is, containing some neighborhood origin), strengthens 1974 result explicitly specifying set Bsh monomials cardinality d!×Vol...