Question

If $\phi:A\to B$ is a ring homomorphism, why does there exist $\psi:\text{spec}(A)\to \text{spec}(B)$?

score 921 · Answer 1 · 2026-04-13 22:10:15

921

Views

If $\phi:A\to B$ is a ring homomorphism, why does there exist $\psi:\text{spec}(A)\to \text{spec}(B)$?

Published on 13 Apr 2026 - 22:10

score 52 · Answer 2 · 2026-04-16 15:15:30

52

Views

Proving $R/J$ is local, where $R=k[\Gamma]$ and $J=(x^1)\unlhd R$.

Published on 16 Apr 2026 - 15:15

score 126 · Answer 3 · 2026-04-15 19:59:50

126

Views

Prove that $m_1m_2\ldots m_r=n_1n_2\ldots n_s$ implies $r=s$ for distinct maximal ideals

Published on 15 Apr 2026 - 19:59

score 156 · Answer 4 · 2026-03-30 01:12:37

156

Views

Correspondence between nilpotents and between idempotents

Published on 30 Mar 2026 - 1:12

score 136 · Answer 5 · 2026-04-10 09:28:14

136

Views

Given a ring $R$, $R=(1)$ is a principal ideal

Published on 10 Apr 2026 - 9:28

score 87 · Answer 6 · 2026-04-14 15:42:42

87

Views

What would an ideal I generated by e.g. 15 and 12 look like? What would the quotient ring $\mathbb{Z} / I$ look like?

Published on 14 Apr 2026 - 15:42

score 1.5k · Answer 7 · 2026-04-12 01:45:20

1.5k

Views

What does the ideal $I$ of $\mathbb{Z}[X]$ generated by $x$ and $2$ look like?

Published on 12 Apr 2026 - 1:45

score 71 · Answer 8 · 2026-04-12 03:05:32

71

Views

$A_i \subset$ ring $R$ st $\Delta A_i \equiv \{ b-c: b,c \in A_i\} = $ an ideal of $R$, then $\bigcap_i (\Delta A_i) = \Delta (\bigcap_i A_i)$.

Published on 12 Apr 2026 - 3:05

score 76 · Answer 9 · 2026-03-11 20:05:52

76

Views

Prove that $\operatorname {ht}(p/a)\leq \operatorname {ht}(p)\leq \operatorname {ht}(p/a)+n$

Published on 11 Mar 2026 - 20:05

score 109 · Answer 10 · 2026-04-13 17:34:17

109

Views

For ideals $I=(8)$ and $J=(5+5i)$ in $\mathbb{Z}[i]$, what are $IJ$, $I+J$ and $I\cap J$?

Published on 13 Apr 2026 - 17:34

score 86 · Answer 11 · 2026-04-13 19:42:37

86

Views

Determine if an ideal is prime

Published on 13 Apr 2026 - 19:42

score 79 · Answer 12 · 2026-04-15 11:49:51

79

Views

Uncountably many left ideals?

Published on 15 Apr 2026 - 11:49

score 2k · Answer 13 · 2026-04-09 17:25:51

2k

Views

Principal Ideals and Identity elements

Published on 09 Apr 2026 - 17:25

score 163 · Answer 14 · 2026-04-12 09:21:46

163

Views

Showing that $\operatorname{lcm}(a,b)$ is the unique positive generator of $(a) \cap (b)$

Published on 12 Apr 2026 - 9:21

score 3k · Answer 15 · 2026-04-09 00:54:26

3k

Views

Is $\mathbb{Z}[\sqrt{15}]$ a UFD?

Published on 09 Apr 2026 - 0:54

List Question

If $\phi:A\to B$ is a ring homomorphism, why does there exist $\psi:\text{spec}(A)\to \text{spec}(B)$?

Proving $R/J$ is local, where $R=k[\Gamma]$ and $J=(x^1)\unlhd R$.

Prove that $m_1m_2\ldots m_r=n_1n_2\ldots n_s$ implies $r=s$ for distinct maximal ideals

Correspondence between nilpotents and between idempotents

Given a ring $R$, $R=(1)$ is a principal ideal

What would an ideal I generated by e.g. 15 and 12 look like? What would the quotient ring $\mathbb{Z} / I$ look like?

What does the ideal $I$ of $\mathbb{Z}[X]$ generated by $x$ and $2$ look like?

$A_i \subset$ ring $R$ st $\Delta A_i \equiv \{ b-c: b,c \in A_i\} = $ an ideal of $R$, then $\bigcap_i (\Delta A_i) = \Delta (\bigcap_i A_i)$.

Prove that $\operatorname {ht}(p/a)\leq \operatorname {ht}(p)\leq \operatorname {ht}(p/a)+n$

For ideals $I=(8)$ and $J=(5+5i)$ in $\mathbb{Z}[i]$, what are $IJ$, $I+J$ and $I\cap J$?

Determine if an ideal is prime

Uncountably many left ideals?

Principal Ideals and Identity elements

Showing that $\operatorname{lcm}(a,b)$ is the unique positive generator of $(a) \cap (b)$

Is $\mathbb{Z}[\sqrt{15}]$ a UFD?

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