Question

Over a commutative ring, $AB = I_n$ and $BA = I_m$ implies that $m = n$.

score 120 · Answer 1 · 2026-04-15 19:39:04

120

Views

Over a commutative ring, $AB = I_n$ and $BA = I_m$ implies that $m = n$.

Published on 15 Apr 2026 - 19:39

score 114 · Answer 2 · 2026-05-10 14:56:40

114

Views

How to show that $a^2+ab+b^2<p$ for integers $a,b$?

Published on 10 May 2026 - 14:56

score 25 · Answer 3 · 2026-04-15 19:29:23

25

Views

Show that $\phi:A/Q\to B/P$ is injective.

Published on 15 Apr 2026 - 19:29

score 73 · Answer 4 · 2026-05-05 16:27:55

73

Views

Proving $I\subseteq\sqrt I$ in a commutative ring

Published on 05 May 2026 - 16:27

score 105 · Answer 5 · 2026-03-25 15:47:22

105

Views

Zerodimensional, compact space is homeomorphic to spectrum of some ring -- elementary attempt

Published on 25 Mar 2026 - 15:47

score 49 · Answer 6 · 2026-03-26 06:02:50

49

Views

Discrete Valuation Property

Published on 26 Mar 2026 - 6:02

score 55 · Answer 7 · 2026-04-16 15:24:00

55

Views

Why does $\langle a \rangle \langle b \rangle \subset \langle ab \rangle$ in a commutative ring?

Published on 16 Apr 2026 - 15:24

score 670 · Answer 8 · 2026-04-16 08:30:42

670

Views

The annihilator $\mathrm{Ann}_R(m)\subseteq R$ is a maximal left ideal of $R$

Published on 16 Apr 2026 - 8:30

score 58 · Answer 9 · 2026-05-05 12:45:45

58

Views

Concerning the ring extension $A[a^{-1}] \subseteq B[a^{-1}] \subseteq C[a^{-1}]$

Published on 05 May 2026 - 12:45

score 61 · Answer 10 · 2026-04-15 02:17:42

61

Views

Artin product rings example

Published on 15 Apr 2026 - 2:17

score 210 · Answer 11 · 2026-05-11 08:40:55

If there exists a positive integer $n$ such that any element $x$ of a ring $R$ satisfies $x^{4^n+2} = x$, then every element $x$ in $R$ is idempotent

score 1k · Answer 12 · 2026-04-14 07:53:24

1k

Views

Irreducible polynomial over field $\mathbb{R}$

Published on 14 Apr 2026 - 7:53

score 191 · Answer 13 · 2026-05-10 19:25:29

191

Views

What is the big picture behind the quotient of a ring by its maximal ideal being a field?

Published on 10 May 2026 - 19:25

score 124 · Answer 14 · 2026-04-12 08:48:05

124

Views

Is it true that $y^7=y$ in a commutative ring with $r^8=r$?

Published on 12 Apr 2026 - 8:48

score 1k · Answer 15 · 2026-04-16 12:47:22

1k

Views

Show that $(x,y)$ is prime and maximal ideal in $\mathbb Q[x,y]$.

Published on 16 Apr 2026 - 12:47

List Question

Over a commutative ring, $AB = I_n$ and $BA = I_m$ implies that $m = n$.

How to show that $a^2+ab+b^2<p$ for integers $a,b$?

Show that $\phi:A/Q\to B/P$ is injective.

Proving $I\subseteq\sqrt I$ in a commutative ring

Zerodimensional, compact space is homeomorphic to spectrum of some ring -- elementary attempt

Discrete Valuation Property

Why does $\langle a \rangle \langle b \rangle \subset \langle ab \rangle$ in a commutative ring?

The annihilator $\mathrm{Ann}_R(m)\subseteq R$ is a maximal left ideal of $R$

Concerning the ring extension $A[a^{-1}] \subseteq B[a^{-1}] \subseteq C[a^{-1}]$

Artin product rings example

If there exists a positive integer $n$ such that any element $x$ of a ring $R$ satisfies $x^{4^n+2} = x$, then every element $x$ in $R$ is idempotent

Irreducible polynomial over field $\mathbb{R}$

What is the big picture behind the quotient of a ring by its maximal ideal being a field?

Is it true that $y^7=y$ in a commutative ring with $r^8=r$?

Show that $(x,y)$ is prime and maximal ideal in $\mathbb Q[x,y]$.

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