In this article, we introduce and study the notion of Goldie dimension for C*-algebras. We prove that a C*-algebra A has Goldie dimension n if and only if the dimension of the center of its local multiplier algebra is n. In this case, A has finite-dimensional center and its primitive spectrum is extremally disconnected. If moreover, A is extending, we show that it decomposes into a direct sum of n prime C*-algebras. In particular, every stably finite, exact C*-algebra with Goldie dimension, that has the projection property and a strictly full element, admits a full projection and a non-zero densely defined lower semi-continuous trace. Finally we show that certain C*-algebras with Goldie dimension (not necessarily simple, separable or nuclear) are classifiable by the Elliott invariant.

在本文中，我们介绍并研究了 C* 代数的 Goldie 维数的概念。我们证明 C* 代数A具有 Goldie 维数n当且仅当其局部乘子代数中心的维数为n。在这种情况下，A具有有限维中心，并且其本原谱是极度不连通的。此外，如果 A 正在扩展，我们证明它可以分解为n 个素数 C* 代数的直和。特别是，每个具有 Goldie 维数的稳定有限、精确 C* 代数，具有投影属性和严格满元素，允许全投影和非零稠密定义的下半连续迹。最后我们证明某些具有 Goldie 维数的 C* 代数（不一定是简单的、可分离的或核的）可以通过艾略特不变量进行分类。