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A commutative diagram that connects the basic objects of commutative algebrawith the main objects of commutative analysis is constructed. Namely, with thehelp of five types of canonical embeddings we constructed a diagram between twosets of objects: Abelian semigroups -- Abelian regular (cancellative)semigroups -- Abelian groups, on the first hand, and convex cones -- regularconvex cones -- linear spaces, on the other hand. Thus, some extension of theGrothendieck algebraic K--theory arises, that includes the basic objects notonly of linear (smooth) analysis but of sublinear (nonsmooth) analysis also.

Sublinear extension of Grothendieck Algebraic K--theory (This paper is dedicated to the 80-th anniversary of Yuri I. Manin)