Question

Showing the set of units $R^{x}$ of a ring with identity $R$ is closed under multiplication.

score 514 · Answer 1 · 2018-10-29 21:36:06

514

Views

Showing the set of units $R^{x}$ of a ring with identity $R$ is closed under multiplication.

Published on 29 Oct 2018 - 21:36

score 147 · Answer 2 · 2026-03-26 04:14:34

147

Views

If $a^{3}=a$ for all $a\in R$, show that the ring $R$ is commutative.

Published on 26 Mar 2026 - 4:14

score 239 · Answer 3 · 2018-10-29 22:47:29

239

Views

A division algorithm for multivariable Laurent polynomials?

Published on 29 Oct 2018 - 22:47

score 371 · Answer 4 · 2026-03-25 06:04:28

371

Views

Write $5$ and $6+8i$ as products of irreducible elements in $\mathbb{Z}[i]$.

Published on 25 Mar 2026 - 6:04

score 167 · Answer 5 · 2018-10-30 02:42:01

167

Views

Are there rings with uncountably many irreducible elements (prime elements, if in a PID)?

Published on 30 Oct 2018 - 2:42

score 1.2k · Answer 6 · 2026-03-26 08:23:01

1.2k

Views

Let $D$ be a PID and $a$ and $b$ be nonzero elements of $D$. Prove that there exist elements $s$ and $t$ in $D$ such that $\gcd(a, b) = as + bt$.

Published on 26 Mar 2026 - 8:23

score 2k · Answer 7 · 2018-10-30 04:52:34

2k

Views

What is Homomorphic image of a field $F$?

Published on 30 Oct 2018 - 4:52

score 276 · Answer 8 · 2018-10-30 13:20:29

276

Views

The only non-trivial Homomorphic images of a field $F$ is $F$-------Is the statement true?

Published on 30 Oct 2018 - 13:20

score 58 · Answer 9 · 2026-04-02 02:10:52

58

Views

Examples of prime-like entities on rings other than natural numbers

Published on 02 Apr 2026 - 2:10

score 160 · Answer 10 · 2018-10-30 14:56:58

160

Views

Describe a residue class R/pR

Published on 30 Oct 2018 - 14:56

score 105 · Answer 11 · 2018-10-30 16:09:01

105

Views

How to describe all the direct sum of Z module $ Z \oplus Z_{2}$?

Published on 30 Oct 2018 - 16:09

score 974 · Answer 12 · 2018-10-30 16:26:17

974

Views

Showing $[\mathbb{Q}(2^{1/3},2^{1/2}):\mathbb{Q}(2^{1/2})]=3$

Published on 30 Oct 2018 - 16:26

score 440 · Answer 13 · 2018-10-30 16:31:12

440

Views

Finding the splitting field $K$ of $x^4+x^2+1$ over $\mathbb{Q}$ and $[K:\mathbb{Q}]$

Published on 30 Oct 2018 - 16:31

score 357 · Answer 14 · 2026-03-25 06:24:29

357

Views

$K(X)$ is not faithfully flat $K[X]$ module.

Published on 25 Mar 2026 - 6:24

score 24 · Answer 15 · 2026-03-25 10:56:00

24

Views

Showing that $(x+y)^2 \in A_1(k)$ does not have a Dixmier mate

Published on 25 Mar 2026 - 10:56

List Question

Showing the set of units $R^{x}$ of a ring with identity $R$ is closed under multiplication.

If $a^{3}=a$ for all $a\in R$, show that the ring $R$ is commutative.

A division algorithm for multivariable Laurent polynomials?

Write $5$ and $6+8i$ as products of irreducible elements in $\mathbb{Z}[i]$.

Are there rings with uncountably many irreducible elements (prime elements, if in a PID)?

Let $D$ be a PID and $a$ and $b$ be nonzero elements of $D$. Prove that there exist elements $s$ and $t$ in $D$ such that $\gcd(a, b) = as + bt$.

What is Homomorphic image of a field $F$?

The only non-trivial Homomorphic images of a field $F$ is $F$-------Is the statement true?

Examples of prime-like entities on rings other than natural numbers

Describe a residue class R/pR

How to describe all the direct sum of Z module $ Z \oplus Z_{2}$?

Showing $[\mathbb{Q}(2^{1/3},2^{1/2}):\mathbb{Q}(2^{1/2})]=3$

Finding the splitting field $K$ of $x^4+x^2+1$ over $\mathbb{Q}$ and $[K:\mathbb{Q}]$

$K(X)$ is not faithfully flat $K[X]$ module.

Showing that $(x+y)^2 \in A_1(k)$ does not have a Dixmier mate

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