Timeline for coprime and strictly coprime ideals
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2018 at 13:34 | vote | accept | CommunityBot | ||
| Feb 10, 2018 at 0:27 | comment | added | M.G. | It's probably worth noting that 'pairwise strictly coprime ideals' are also known as 'pairwise comaximal ideals'. | |
| Feb 9, 2018 at 20:29 | comment | added | anon | Actually, Milne doesn't use "two notions: coprime ideals and strictly coprime ideals". He only talks about strictly coprime polynomials. See Billy's post. | |
| Feb 9, 2018 at 18:56 | comment | added | LSpice | @ZSun, your statement "every reference I saw …" is false by example, because the claim is that Milne is using the term in a different way. I agree that I think that your use is more standard, but there's no point arguing about it once we know what Milne actually meant. | |
| Feb 9, 2018 at 18:46 | answer | added | Billy | timeline score: 3 | |
| Feb 9, 2018 at 17:13 | comment | added | user111251 | Wojowu i see...but every reference i saw says that I and J are said to be coprime if I+J=the whole ring ...this condition is same as saying that (I,J)=whole ring...anyway thanks | |
| Feb 9, 2018 at 17:05 | comment | added | Wojowu | The notion of divisibility makes sense in every commutative ring. Then we just say there is no non-unit which divides both elements. | |
| Feb 9, 2018 at 17:04 | comment | added | user111251 | @Wojowu i see...but how would you define "this common factor " condition for general commutative ring?? | |
| Feb 9, 2018 at 17:01 | comment | added | Wojowu | I believe we have coprime = have no common factors and strictly coprime = together generate the whole ring. The difference can be seen in the case of $\mathbb Z[x]$, where $2,x$ have no common factors, but $1\not\in(2,x)$. | |
| Feb 9, 2018 at 16:43 | history | asked | user111251 | CC BY-SA 3.0 |