Question

Let $R$, $S$ be rings with identity and $f: R\to S$ a homomorphism. Is there a name for the this subset of the units of $R$?

score 65 · Answer 1 · 2026-04-15 14:00:39

65

Views

Let $R$, $S$ be rings with identity and $f: R\to S$ a homomorphism. Is there a name for the this subset of the units of $R$?

Published on 15 Apr 2026 - 14:00

score 141 · Answer 2 · 2026-04-16 21:30:01

141

Views

Homomorphisms between $\mathbb {F_p}$ and $\mathbb F_{p^2} \bigoplus \mathbb F_p$.

Published on 16 Apr 2026 - 21:30

score 1.9k · Answer 3 · 2026-04-14 08:15:05

1.9k

Views

Let $R$ be a commutative ring with unity, prove that $I$ is an ideal of $R$.

Published on 14 Apr 2026 - 8:15

score 90 · Answer 4 · 2026-04-17 10:11:06

90

Views

Clean ring decomposition

Published on 17 Apr 2026 - 10:11

score 76 · Answer 5 · 2026-05-11 08:52:11

76

Views

Are $3\mathbb {Z}$ and $9\mathbb {Z}$ ring isomorphic?

Published on 11 May 2026 - 8:52

score 113 · Answer 6 · 2026-05-10 15:18:33

113

Views

Nilpotents in a domain?

Published on 10 May 2026 - 15:18

score 87 · Answer 7 · 2026-04-14 16:05:11

87

Views

If $X$ is a nonempty subset of $R$, show that $C(X) = \{c \in R \mid cx = xc \;\;\forall x \in X\}$ is a subring of $R$.

Published on 14 Apr 2026 - 16:05

score 46 · Answer 8 · 2026-04-15 10:11:41

46

Views

Finding a Degree Function: Let $R=\Bbb Z[i]$ and let $d(x)=N(x)$ for $x∈R$, where $N(x)$ is the norm of $x$

Published on 15 Apr 2026 - 10:11

score 381 · Answer 9 · 2026-04-17 01:53:39

381

Views

If $A$ is an ideal of $R$, show that $R/A$ is commutative if and only if $rs - sr \in A$ for all $r, s\in R$.

Published on 17 Apr 2026 - 1:53

score 130 · Answer 10 · 2026-05-11 09:32:55

130

Views

What is the motivation for $R$-algebras?

Published on 11 May 2026 - 9:32

score 41 · Answer 11 · 2026-04-16 08:44:12

41

Views

Fix a prime and let $R=$ {$m/n \in \mathbb Q: m,n \in \mathbb Z$},where $p$ does not divide $n$. Show that $R$ is local.

Published on 16 Apr 2026 - 8:44

score 79 · Answer 12 · 2026-04-08 04:51:54

79

Views

Strictly increasing chain of ideals in continuous functions on [0,1].

Published on 08 Apr 2026 - 4:51

score 123 · Answer 13 · 2026-03-27 07:20:02

123

Views

How can I show that a specific object is cofibrant in $s\mathbf{Alg}_{R}$?

Published on 27 Mar 2026 - 7:20

score 43 · Answer 14 · 2026-04-16 08:33:32

43

Views

Attempt to sketch a proof showing $M$ is not projective given $M$ is a $\mathbb{Q}[x]-module$ such that $dim_{\mathbb{Q}}(M) < \inf$

Published on 16 Apr 2026 - 8:33

score 86 · Answer 15 · 2026-04-09 19:14:59

86

Views

Finding the class number of $K$

Published on 09 Apr 2026 - 19:14

List Question

Let $R$, $S$ be rings with identity and $f: R\to S$ a homomorphism. Is there a name for the this subset of the units of $R$?

Homomorphisms between $\mathbb {F_p}$ and $\mathbb F_{p^2} \bigoplus \mathbb F_p$.

Let $R$ be a commutative ring with unity, prove that $I$ is an ideal of $R$.

Clean ring decomposition

Are $3\mathbb {Z}$ and $9\mathbb {Z}$ ring isomorphic?

Nilpotents in a domain?

If $X$ is a nonempty subset of $R$, show that $C(X) = \{c \in R \mid cx = xc \;\;\forall x \in X\}$ is a subring of $R$.

Finding a Degree Function: Let $R=\Bbb Z[i]$ and let $d(x)=N(x)$ for $x∈R$, where $N(x)$ is the norm of $x$

If $A$ is an ideal of $R$, show that $R/A$ is commutative if and only if $rs - sr \in A$ for all $r, s\in R$.

What is the motivation for $R$-algebras?

Fix a prime and let $R=$ {$m/n \in \mathbb Q: m,n \in \mathbb Z$},where $p$ does not divide $n$. Show that $R$ is local.

Strictly increasing chain of ideals in continuous functions on [0,1].

How can I show that a specific object is cofibrant in $s\mathbf{Alg}_{R}$?

Attempt to sketch a proof showing $M$ is not projective given $M$ is a $\mathbb{Q}[x]-module$ such that $dim_{\mathbb{Q}}(M) < \inf$

Finding the class number of $K$

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