电晕分解性质与加细幺半群
The Corona Factorization Property and Refinement Monoids
摘要：
C*-代数的Corona分解性质最初是为了研究C* 代数的扩张而定义的，现在已经证明它对C* 代数的内在结构性质有重要意义.本文证明了实秩为零的σ-有单位的C* 代数-代数A具有Corona分解性质当且仅当A上的矩阵代数的投影的Murray-von Neumann等价类的么半群V（A）具有某种（相当弱的）可比性质，我们称之为Corona分解性质（对于么半群）.我们证明了这样的C* 代数中的投影是真无限的当（且仅当）它的一个倍数是真无限的。后一个结果是从我们建立的关于锥加细幺半群的一些更一般的结果中得到的。我们证明了锥加细么半群中的序单位集（连同零元）在满足弱整除性的假设下也是加细么半群;如果u是加细么半群中的元素，使得nu真的无限大，则u可以写成和u = s + t，使得ns和nt真的无限大。
英文摘要：
The Corona Factorization Property of a C*-algebra, originally defined to study extensions of C*-algebras, has turned out to say something important about intrinsic structural properties of the C*-algebra. We show in this paper that a σ-unital C*-algebra A of real rank zero has the Corona Factorization roperty if and only if its monoid V(A) of Murray-von Neumann equivalence classes of projections in matrix algebras over A has a certain (rather weak) comparability property that we call the Corona Factorization Property (for monoids). We show that a projection in such a C*-algebra is properly infinite if (and only if) a multiple of it is properly infinite. The latter result is obtained from some more general result we establish about conical refinement monoids. We show that the set of order units (together with the zero-element) in a conical refinement monoid is again a refinement monoid under the assumption that the monoid satisfies weak divisibility; and if u is an element in a refinement monoid such that nu is properly infinite, then u can be written as a sum u = s + t such that ns and nt are properly infinite.
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