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

K. R. GoodearlDavid HandelmanJohn W. Lawrence

出版	American Mathematical Soc., 1980
主題	Mathematics / GeneralMathematics / Algebra / General
ISBN	08218223499780821822340
URL	http://books.google.com.hk/books?id=nxzUCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.