Abstract
Levy [2] has examined semiprime rings which are irredundant subdirect products of prime rings. In this note we look at the role of inessential prime ideals and see how every semiprime ring is a subdirect product of (i) a semiprime ring which is an irredundant subdirect product of prime rings, and (ii) a semiprime (nonprime) ring, all of whose prime ideals are essential. This leads to a direct sum decomposition of maximal left quotient rings of semiprime rings with left singular ideal zero.
| Original language | English |
|---|---|
| Pages (from-to) | 176-180 |
| Number of pages | 5 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 46 |
| Issue number | 2 |
| DOIs | |
| State | Published - Nov 1974 |
| Externally published | Yes |
Keywords
- Essential
- Injective hull
- Maximal quotient ring
- Semiprime
- Singular ideal
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