## On the maximal spectrum of commutative semiprimitive rings

### Volume 83 / 2000

Colloquium Mathematicum 83 (2000), 5-13
DOI: 10.4064/cm-83-1-5-13

#### Abstract

The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).