Question

Show that every maximal ideal of $R$ contains the element $a$.

score 466 · Answer 1 · 2026-03-25 11:33:00

466

Views

Show that every maximal ideal of $R$ contains the element $a$.

Published on 25 Mar 2026 - 11:33

score 46 · Answer 2 · 2018-10-15 11:17:54

46

Views

Semisimple matrix ring

Published on 15 Oct 2018 - 11:17

score 95 · Answer 3 · 2026-03-25 03:00:39

95

Views

$R$ a $PID \Rightarrow R[[X]]$ a $UFD$

Published on 25 Mar 2026 - 3:00

score 610 · Answer 4 · 2018-10-15 22:05:04

610

Views

Rings with decomposition are sums of ideals generated by idempotents

Published on 15 Oct 2018 - 22:05

score 133 · Answer 5 · 2026-03-25 04:41:31

133

Views

Given $a, b$ coprime integers, show that any factor of $a^2 - 2b^2$ is of the form $c^2 - 2d^2$

Published on 25 Mar 2026 - 4:41

score 119 · Answer 6 · 2018-10-16 07:29:16

119

Views

Sum, difference and product of algebraic elements is an algebraic element.

Published on 16 Oct 2018 - 7:29

score 157 · Answer 7 · 2026-03-25 10:55:44

157

Views

Division on a real quadratic ring of integers.

Published on 25 Mar 2026 - 10:55

score 233 · Answer 8 · 2018-10-16 16:18:12

233

Views

Let $\alpha: F \rightarrow F$ be a one to one field homomorphism, prove $\alpha$ fixes the prime subfield of $F$ elementwise

Published on 16 Oct 2018 - 16:18

score 682 · Answer 9 · 2018-10-16 16:36:48

682

Views

In a ring with identity, prove that (−1) · (−1)= 1.

Published on 16 Oct 2018 - 16:36

score 79 · Answer 10 · 2018-10-16 22:35:26

79

Views

Use induction to prove that $(a+b)^{p^n}=a^{p^n}+b^{p^n}$

Published on 16 Oct 2018 - 22:35

score 70 · Answer 11 · 2018-10-16 22:37:47

70

Views

Expressiong $\frac{t+2}{t^3+3}$ in the form $a_o+a_1t+...+a_4t^4$, where $t$ is a root of $x^5+2x+2$

Published on 16 Oct 2018 - 22:37

score 65 · Answer 12 · 2018-10-16 23:19:40

65

Views

Is my solution correct on this Groups/Rings

Published on 16 Oct 2018 - 23:19

score 31 · Answer 13 · 2026-03-28 11:44:13

31

Views

If $R$ is a ring such that $x^2=x$ $\forall x \in R$ and $I$ is a prime ideal. Show that $R/I$ has two elements

Published on 28 Mar 2026 - 11:44

score 349 · Answer 14 · 2018-10-17 03:44:31

349

Views

In the ring $\Bbb Z_6$ commutative ring with $1$,why $[3]$ is not irreducible?

Published on 17 Oct 2018 - 3:44

score 389 · Answer 15 · 2026-03-25 09:23:55

389

Views

Rings isomorphic to a proper subring

Published on 25 Mar 2026 - 9:23

List Question

Show that every maximal ideal of $R$ contains the element $a$.

Semisimple matrix ring

$R$ a $PID \Rightarrow R[[X]]$ a $UFD$

Rings with decomposition are sums of ideals generated by idempotents

Given $a, b$ coprime integers, show that any factor of $a^2 - 2b^2$ is of the form $c^2 - 2d^2$

Sum, difference and product of algebraic elements is an algebraic element.

Division on a real quadratic ring of integers.

Let $\alpha: F \rightarrow F$ be a one to one field homomorphism, prove $\alpha$ fixes the prime subfield of $F$ elementwise

In a ring with identity, prove that (−1) · (−1)= 1.

Use induction to prove that $(a+b)^{p^n}=a^{p^n}+b^{p^n}$

Expressiong $\frac{t+2}{t^3+3}$ in the form $a_o+a_1t+...+a_4t^4$, where $t$ is a root of $x^5+2x+2$

Is my solution correct on this Groups/Rings

If $R$ is a ring such that $x^2=x$ $\forall x \in R$ and $I$ is a prime ideal. Show that $R/I$ has two elements

In the ring $\Bbb Z_6$ commutative ring with $1$,why $[3]$ is not irreducible?

Rings isomorphic to a proper subring

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