Question

Simple rings/algebras fail to be division rings/algebras because of zero-divisors?

score 50 · Answer 1 · 2023-04-11 13:00:42

50

Views

Simple rings/algebras fail to be division rings/algebras because of zero-divisors?

Published on 11 Apr 2023 - 13:00

score 240 · Answer 2 · 2026-03-26 01:25:14

240

Views

Is the ideal generated by coefficients of characteristic polynomial of a matrix prime?

Published on 26 Mar 2026 - 1:25

score 48 · Answer 3 · 2023-04-19 13:49:31

48

Views

Maximal ideal $M$ is prime in commutative (non unital) ring A such that $A^2\neq0$.

Published on 19 Apr 2023 - 13:49

score 100 · Answer 4 · 2026-03-29 03:03:48

100

Views

Extension and contraction of prime ideals by ring homomorphism

Published on 29 Mar 2026 - 3:03

score 298 · Answer 5 · 2023-04-22 23:11:05

298

Views

For a maximal ideal $I$, does $rs \in I^n$ and $s \not \in I$ imply $r \in I^n$?

Published on 22 Apr 2023 - 23:11

score 38 · Answer 6 · 2023-05-02 14:06:40

38

Views

Goldman ideal as an isolated prime through a special ring map.

Published on 02 May 2023 - 14:06

score 48 · Answer 7 · 2026-03-25 17:39:18

48

Views

What exactly is the relationship between associated primes and the radical ideal?

Published on 25 Mar 2026 - 17:39

score 66 · Answer 8 · 2023-05-07 06:01:30

66

Views

Can we determine maximal ideals of $\mathbb{Z}[x, y]$ by using $\mathbb{Z}[x] \subset \mathbb{Z}[x, y]$?

Published on 07 May 2023 - 6:01

score 27 · Answer 9 · 2026-03-25 16:01:48

27

Views

Preimage of a maximal ideal is maximal in free ring extensions

Published on 25 Mar 2026 - 16:01

score 114 · Answer 10 · 2026-03-25 21:47:31

114

Views

Prime & Maximal Ideal in $\mathbb{Z}[x]$

Published on 25 Mar 2026 - 21:47

score 45 · Answer 11 · 2023-05-16 22:34:55

45

Views

J maximal of a direct sum.

Published on 16 May 2023 - 22:34

score 86 · Answer 12 · 2026-03-29 07:00:33

86

Views

Intuitively, why $\operatorname{spec}(S^{-1}A) \cong \lbrace \mathfrak{p} \in \operatorname{spec} (A)| \mathfrak{p} \cap S = \emptyset \rbrace$?

Published on 29 Mar 2026 - 7:00

score 42 · Answer 13 · 2023-05-22 11:58:28

42

Views

The characteristic of the quotient fields of $\mathbb{Z}[x_1,\ldots, x_n]$

Published on 22 May 2023 - 11:58

score 52 · Answer 14 · 2026-03-25 08:51:44

52

Views

Prove that every ideal of $\Bbb{Z}$ has the form $m\Bbb{Z}=\{mk, k\in \Bbb{Z}\}$

Published on 25 Mar 2026 - 8:51

score 125 · Answer 15 · 2023-06-21 11:24:10

125

Views

When are the UFD, PID hypothesis needed in this proof?

Published on 21 Jun 2023 - 11:24

List Question

Simple rings/algebras fail to be division rings/algebras because of zero-divisors?

Is the ideal generated by coefficients of characteristic polynomial of a matrix prime?

Maximal ideal $M$ is prime in commutative (non unital) ring A such that $A^2\neq0$.

Extension and contraction of prime ideals by ring homomorphism

For a maximal ideal $I$, does $rs \in I^n$ and $s \not \in I$ imply $r \in I^n$?

Goldman ideal as an isolated prime through a special ring map.

What exactly is the relationship between associated primes and the radical ideal?

Can we determine maximal ideals of $\mathbb{Z}[x, y]$ by using $\mathbb{Z}[x] \subset \mathbb{Z}[x, y]$?

Preimage of a maximal ideal is maximal in free ring extensions

Prime & Maximal Ideal in $\mathbb{Z}[x]$

J maximal of a direct sum.

Intuitively, why $\operatorname{spec}(S^{-1}A) \cong \lbrace \mathfrak{p} \in \operatorname{spec} (A)| \mathfrak{p} \cap S = \emptyset \rbrace$?

The characteristic of the quotient fields of $\mathbb{Z}[x_1,\ldots, x_n]$

Prove that every ideal of $\Bbb{Z}$ has the form $m\Bbb{Z}=\{mk, k\in \Bbb{Z}\}$

When are the UFD, PID hypothesis needed in this proof?

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