Question

Ring homomorphism with field as image, is the pre-image also a field?

score 798 · Answer 1 · 2026-04-09 06:02:49

798

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Ring homomorphism with field as image, is the pre-image also a field?

Published on 09 Apr 2026 - 6:02

score 619 · Answer 2 · 2026-03-25 15:47:24

619

Views

Every irreducible element is prime: always holds under surjective ring homomorphism?

Published on 25 Mar 2026 - 15:47

score 108 · Answer 3 · 2026-04-12 19:16:41

108

Views

Topological closure of ideal in $A[[T]]$ - Proposition 1.3.7 in Liu

Published on 12 Apr 2026 - 19:16

score 870 · Answer 4 · 2014-03-30 16:34:39

870

Views

If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.

Published on 30 Mar 2014 - 16:34

score 6k · Answer 5 · 2026-03-27 16:27:41

6k

Views

Prove $x^3-3x+4$ is irreducible in $\mathbb{Q}[x]$

Published on 27 Mar 2026 - 16:27

score 81 · Answer 6 · 2026-04-13 10:48:36

81

Views

Complexifications of degree 3 subschemes in $\mathbb A^2_{\mathbb R}$

Published on 13 Apr 2026 - 10:48

score 4.7k · Answer 7 · 2026-04-11 18:09:56

4.7k

Views

Is this quotient Ring Isomorphic to the Complex Numbers

Published on 11 Apr 2026 - 18:09

score 1.5k · Answer 8 · 2026-04-13 07:26:01

1.5k

Views

When an Intersection of Prime Ideals is a Prime Ideal

Published on 13 Apr 2026 - 7:26

score 742 · Answer 9 · 2014-03-30 23:05:20

742

Views

A commutative ring $R$ is local if and only if, for all $r,s\in R$, $r+s=1$ implies $r$ or $s$ is a unit.

Published on 30 Mar 2014 - 23:05

score 279 · Answer 10 · 2026-04-11 02:37:36

279

Views

A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$

Published on 11 Apr 2026 - 2:37

score 854 · Answer 11 · 2026-03-30 00:19:13

854

Views

When does $x^{q'}-x$ divide $x^q-x$ in $\mathbb{Z}[x]$?

Published on 30 Mar 2026 - 0:19

score 107 · Answer 12 · 2026-04-12 21:28:50

107

Views

Is the restricted enveloping algebra local?

Published on 12 Apr 2026 - 21:28

score 181 · Answer 13 · 2026-04-12 10:14:51

181

Views

Number of isomorphisms between two fields

Published on 12 Apr 2026 - 10:14

score 82 · Answer 14 · 2026-04-04 05:35:44

82

Views

why $RM \neq 0$

Published on 04 Apr 2026 - 5:35

score 121 · Answer 15 · 2026-03-26 06:12:43

121

Views

Need some help finishing this proof about characters in Banach algebras

Published on 26 Mar 2026 - 6:12

List Question

Ring homomorphism with field as image, is the pre-image also a field?

Every irreducible element is prime: always holds under surjective ring homomorphism?

Topological closure of ideal in $A[[T]]$ - Proposition 1.3.7 in Liu

If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.

Prove $x^3-3x+4$ is irreducible in $\mathbb{Q}[x]$

Complexifications of degree 3 subschemes in $\mathbb A^2_{\mathbb R}$

Is this quotient Ring Isomorphic to the Complex Numbers

When an Intersection of Prime Ideals is a Prime Ideal

A commutative ring $R$ is local if and only if, for all $r,s\in R$, $r+s=1$ implies $r$ or $s$ is a unit.

A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$

When does $x^{q'}-x$ divide $x^q-x$ in $\mathbb{Z}[x]$?

Is the restricted enveloping algebra local?

Number of isomorphisms between two fields

why $RM \neq 0$

Need some help finishing this proof about characters in Banach algebras

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