# On the maximal spectrum of commutative semiprimitive rings

Colloquium Mathematicae (2000)

- Volume: 83, Issue: 1, page 5-13
- ISSN: 0010-1354

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topSamei, K.. "On the maximal spectrum of commutative semiprimitive rings." Colloquium Mathematicae 83.1 (2000): 5-13. <http://eudml.org/doc/210774>.

@article{Samei2000,

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).},

author = {Samei, K.},

journal = {Colloquium Mathematicae},

keywords = {spectrum of a ring; maximal ideal space},

language = {eng},

number = {1},

pages = {5-13},

title = {On the maximal spectrum of commutative semiprimitive rings},

url = {http://eudml.org/doc/210774},

volume = {83},

year = {2000},

}

TY - JOUR

AU - Samei, K.

TI - On the maximal spectrum of commutative semiprimitive rings

JO - Colloquium Mathematicae

PY - 2000

VL - 83

IS - 1

SP - 5

EP - 13

AB - 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).

LA - eng

KW - spectrum of a ring; maximal ideal space

UR - http://eudml.org/doc/210774

ER -

## References

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- [10] S. H. Sun, Noncommutative rings in which every prime ideal is contained in a unique maximal ideal, J. Pure Appl. Algebra 76 (1991), 179-192. Zbl0747.16001
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