In this paper, we describe the Grothendieck group $$K_0(V)$$ of an absolute matrix order unit space V. For purpose, discuss direct limit spaces. We show that $$K_0$$ is a functor from category spaces with morphisms as unital completely $$\vert \cdot \vert$$ -preserving maps to abelian groups. study structure in and prove under certain condition, ordered group. also additive on orthogonal maps.

Abstract Let R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on is ring with pointwise operations. Its group units $${{\mathcal{F}}}(R)^\times $$ × j...

Group buying is a business model in which a number of buyers join together to make an order of a product in a certain quantity in order to gain a desirable discounted price. Such a business model has recently received significant attention from researchers in economics and computer science, mostly due to its successful application in online businesses, such as Groupon5. This paper deals with th...