Timeline for Monomial order and prime ideals
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2022 at 22:45 | comment | added | pinaki | Well, it is possible that $I$ is prime, but $in_<(I)$ is radical, but not prime, e.g. when $I$ is the ideal generated by $x_1x_2 - x_3^2$ and $<$ is a monomial order such that $x_1x_2 < x_3^2$. | |
| Mar 22, 2022 at 20:56 | comment | added | Wágner Badilla | Yes, see Lemma 1.2.5. Book A singular introduction to commutaitva algebra. | |
| Mar 22, 2022 at 20:48 | comment | added | markvs | Is that proved somewhere? | |
| Mar 22, 2022 at 20:45 | comment | added | Wágner Badilla | The global monomial order implies well order. | |
| Mar 22, 2022 at 20:44 | comment | added | Wágner Badilla | $x^{\alpha}=x_1^{\alpha_1}\cdots x_n^{\alpha_n}$ with $\alpha=(\alpha_1,\ldots,\alpha_n) \in \mathbb{Z}_{\geq 0}^n$, $\alpha \not=0$. | |
| Mar 22, 2022 at 20:17 | comment | added | markvs | I do not know what is $x^\alpha$ (or even what is $\alpha$)? And why does it imply "well order".Total order just means linear order. | |
| Mar 22, 2022 at 19:40 | comment | added | Wágner Badilla | Is that $<$ is a total order, $1<x^{\alpha}$, and $<$ respects multiplication by monomials. | |
| Mar 22, 2022 at 19:37 | comment | added | markvs | What is a "global monomial order"? | |
| Mar 22, 2022 at 19:28 | history | edited | Wágner Badilla | CC BY-SA 4.0 |
added 84 characters in body
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| Mar 22, 2022 at 19:26 | comment | added | Wágner Badilla | I assume that $<$ is a global monomial order. Thus, $<$ is a well order. | |
| Mar 22, 2022 at 19:23 | comment | added | markvs | There are two different definitions of "monomial order". Do you assume that $<$ is a well order? | |
| Mar 22, 2022 at 19:18 | comment | added | Wágner Badilla | To be specific. Suppose $in_<(I)$ is a radical ideal. Let $P_1, \ldots, P_t$ be the minimal prime ideals of $I$. Then, $in_<(P_1), \ldots,in_<(P_t)$ are the minimal prime ideals of $in_<(i)$. Is this true? | |
| Mar 22, 2022 at 4:55 | comment | added | markvs | Depends on "<"? | |
| S Mar 22, 2022 at 2:54 | review | First questions | |||
| Mar 22, 2022 at 7:31 | |||||
| S Mar 22, 2022 at 2:54 | history | asked | Wágner Badilla | CC BY-SA 4.0 |