Timeline for From reducible polynomial to an irreducible one
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 7, 2013 at 18:31 | answer | added | Kevin O'Bryant | timeline score: 1 | |
| Mar 7, 2013 at 17:24 | answer | added | Peter Mueller | timeline score: 2 | |
| Mar 7, 2013 at 16:39 | answer | added | Joël | timeline score: 1 | |
| Mar 7, 2013 at 16:37 | comment | added | user9072 | Except on second though, in principle, one could do somethings like this, via localising the polynomial ring appropriately so that all but one factor will become invertible; this might work always except for the polynomial being a perfect power in the ring of polynomials. But then you get something quite different with this. Yet perhaps you meant this. | |
| Mar 7, 2013 at 16:31 | comment | added | user9072 | I am not completely sure I understand what you mean. But extending the field from Q to something larger could make an irreducible polynomial reducible, yet not the converse. (You have 'more' choices for factors.) One might consider the eplynomial over a subring of Q, but then Z is the smallest one and then by Gauss's Lemma (except for 'constants') regarding irreducibility nothing changes. So, if I understand the question correctly then, no this is not possible, and you might find Gauss's Lemma interesting. But perhaps I misunderstand this question. | |
| Mar 7, 2013 at 16:03 | history | asked | bruco | CC BY-SA 3.0 |