Affine Representations Of Grothendieck Groups And Applications To Rickart C Algebras And Hebrew Aleph Continuous Regular Rings

Affine Representations of Grothendieck Groups and Applications to Rickart $C^\ast $-Algebras and $\aleph _0$-Continuous Regular Rings

This paper is concerned with the structure of three interrelated classes of objects: partially ordered abelian groups with countable interpolation, [Hebrew]Aleph0-continuous regular rings, and finite Rickart C*-algebras. The connection from these rings and algebras to these groups is the Grothendieck group K0, which, for all [Hebrew]Aleph0-continuous regular rings and most finite Rickart C*-algebras, is a partially ordered abelian group with countable interpolation. Such partially ordered groups are shown to possess quite specific representations in spaces of affine continuous functions on Choquet simplices. The theme of this paper is to develop the structure theory of these groups and these representations, and to translate the results, via K0, into properties of [Hebrew]Aleph0-continuous regular rings and finite Rickart C*-algebras.

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Affine Representations of Grothendieck Groups and Applications to Rickart C*-algebras and [Hebrew Aleph]-continuous Regular Rings