Sublinear extension of algebraic grothendieck theory

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.