Question

Ring with unity. Show that if ab units, then a and b are units.

score 4.6k · Answer 1 · 2018-10-12 15:49:54

4.6k

Views

Ring with unity. Show that if ab units, then a and b are units.

Published on 12 Oct 2018 - 15:49

score 37 · Answer 2 · 2018-10-12 17:38:56

37

Views

In case of prime ring $R$ , the set $ I = R_{12}R_{21} + R_{12} + R_{21} + R_{21}R_{12} $ is an ideal of the ring $R$.

Published on 12 Oct 2018 - 17:38

score 84 · Answer 3 · 2026-03-28 00:05:57

84

Views

A special kind of rings

Published on 13 Oct 2018 - 15:02

score 901 · Answer 5 · 2018-10-13 20:33:51

901

Views

Universal Property of Quotient Field

Published on 13 Oct 2018 - 20:33

score 140 · Answer 6 · 2018-10-14 05:04:54

140

Views

Given $\phi:R\to R/N$, why is the image of a proper ideal containing $N$ proper in $R/N$?

Published on 14 Oct 2018 - 5:04

score 302 · Answer 7 · 2026-03-28 10:04:28

302

Views

Ideals of $\Bbb{Z}_4[X]/(X^2+X+1)$

Published on 28 Mar 2026 - 10:04

score 327 · Answer 8 · 2026-03-29 17:07:15

327

Views

Show that the ring of upper triangular 2x2 matrices is a direct sum of two of its modules

Published on 29 Mar 2026 - 17:07

score 164 · Answer 9 · 2026-04-01 11:00:13

164

Views

Set Ring and Algebraic Ring

Published on 01 Apr 2026 - 11:00

score 105 · Answer 10 · 2026-03-27 09:49:35

105

Views

Looking for a pair of adjoint functors

Published on 27 Mar 2026 - 9:49

score 54 · Answer 11 · 2018-10-14 16:34:52

54

Views

Prove that $\left(\forall\ a \in A \right)\ aTe = eTa = e$

Published on 14 Oct 2018 - 16:34

score 170 · Answer 12 · 2026-03-25 23:38:34

170

Views

Action of sum of traspositions on a simple $\mathbb{C}[S_n]$-module

Published on 25 Mar 2026 - 23:38

score 2.3k · Answer 13 · 2018-10-15 00:00:05

2.3k

Views

$(1-ba)$ left-invertible $\implies (1-ab)$ left-invertible

Published on 15 Oct 2018 - 0:00

score 211 · Answer 14 · 2026-03-29 17:11:49

211

Views

If $r$ is a nilpotent element of a commutative ring $R$ then $(r)$ is not a direct summand of $R$ as an $R$-module.

Published on 29 Mar 2026 - 17:11

score 45 · Answer 15 · 2018-10-15 10:08:52

$R$ is a ring with $\operatorname{char}(R)=mn$ where $(m,n)=1$, then there exists an ideal $A$ such that $\operatorname{char}(A)=m$?

List Question

Ring with unity. Show that if ab units, then a and b are units.

In case of prime ring $R$ , the set $ I = R_{12}R_{21} + R_{12} + R_{21} + R_{21}R_{12} $ is an ideal of the ring $R$.

Suggested Reading? Applications of the Krull-Schmidt Theorem for Groups

A special kind of rings

Universal Property of Quotient Field

Given $\phi:R\to R/N$, why is the image of a proper ideal containing $N$ proper in $R/N$?

Ideals of $\Bbb{Z}_4[X]/(X^2+X+1)$

Show that the ring of upper triangular 2x2 matrices is a direct sum of two of its modules

Set Ring and Algebraic Ring

Looking for a pair of adjoint functors

Prove that $\left(\forall\ a \in A \right)\ aTe = eTa = e$

Action of sum of traspositions on a simple $\mathbb{C}[S_n]$-module

$(1-ba)$ left-invertible $\implies (1-ab)$ left-invertible

If $r$ is a nilpotent element of a commutative ring $R$ then $(r)$ is not a direct summand of $R$ as an $R$-module.

$R$ is a ring with $\operatorname{char}(R)=mn$ where $(m,n)=1$, then there exists an ideal $A$ such that $\operatorname{char}(A)=m$?

Trending Questions

Popular # Hahtags

Popular Questions