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Subdirectly irreducible rings–some pathology
| Content Provider | Scilit |
|---|---|
| Author | Moore, H. G. |
| Copyright Year | 1969 |
| Description | Every ring is isomorphic to a subdirect sum of subdirectly irreducible rings. Unfortunately, however, as is shown, the property of being subdirectly irreducible is not preserved under homomorphisms. An example is given of a finite non-commutative subdirectly irreducible ring R with heart (= the intersection of all non-zero ideals) H, such that R/E is isomorphic with GF(2) + GF(2). (GF(2) is the two element Galois Field.) Some additional properties of the ring R are listed and contrasts are made with results for commutative subdirectly irreducible rings; for example, the zero divisors of R do not form an ideal. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CDB36A47B2BA838F3502F2718ED858F8/S0004972700042246a.pdf/div-class-title-subdirectly-irreducible-rings-some-pathology-div.pdf |
| Ending Page | 355 |
| Page Count | 3 |
| Starting Page | 353 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700042246 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 3 |
| Volume Number | 1 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1969-04-17 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Irreducible Rings Subdirectly Irreducible |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
