  A commutative diagram that connects the basic objects of commutative algebra
with the main objects of commutative analysis is constructed. Namely, with the
help of five types of canonical embeddings we constructed a diagram between two
sets of objects: Abelian semigroups -- Abelian regular (cancellative)
semigroups -- Abelian groups, on the first hand, and convex cones -- regular
convex cones -- linear spaces, on the other hand. Thus, some extension of the
Grothendieck algebraic K--theory arises, that includes the basic objects not
only of linear (smooth) analysis but of sublinear (nonsmooth) analysis also.
