Suppose there exists a sequence of mutually orthogonal and equivalent(projections)idempotents e1,…,en,in the(∗-)ring R,if letting e=e1+…+en,then the ring eRe(∗-)is isomorphic to the full matrix ring Mn(ei Rei),for i=1,…,n.As a result,this paper proves the following results:(1)every truly infinite C∗-algebra∗-is isomorphic to a full matrix algebra;(2)Let M be a von Neumann algebra without exchangeable direct sum terms and LS(M)be the entirety of locally measurable operators attached to M.Then any subalgebra of LS(M)containing M is isomorphic to the direct sum of a sequence of full matrix algebras.
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