论文标题
Morita等效的局部矩阵代数
Morita equivalent unital locally matrix algebras
论文作者
论文摘要
我们描述了Unital局部矩阵代数的Morita等效性，其steinitz参数化。当且仅当其steinitz的数字合理地连接时，两个可计数的局部局部矩阵代数是莫里塔等效的。对于任意的无数尺寸$α$和一个任意的不是本地有限的steinitz $ s $ s $，存在unitial intility artility astrix代数$ a $ a $，$ b $，以至于$ \ dim_ {f} a = \ dim_ {f} a = \ dim_ {f} $ a $，$ b $不是同等的。
We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable dimensional unital locally matrix algebras are Morita equivalent if and only if their Steinitz numbers are rationally connected. For an arbitrary uncountable dimension $α$ and an arbitrary not locally finite Steinitz number $s$ there exist unital locally matrix algebras $A$, $B$ such that $\dim_{F}A=\dim_{F}B=α$, $\mathbf{st}(A)=\mathbf{st}(B)=s$, however, the algebras $A$, $B$ are not Morita equivalent.
