Question

What is the monoid ring $K[(\Bbb{N}, \text{lcm})]$ isomorphic to?

score 42 · Answer 1 · 2026-03-25 17:37:45

42

Views

What is the monoid ring $K[(\Bbb{N}, \text{lcm})]$ isomorphic to?

Published on 25 Mar 2026 - 17:37

score 68 · Answer 2 · 2023-06-02 11:23:30

68

Views

Do isomorphisms of quotients of polynomial rings by monomial ideal preserve the constants?

Published on 02 Jun 2023 - 11:23

score 87 · Answer 3 · 2023-06-03 06:46:50

87

Views

show $\mathbb{Q}[t]/(t^2-1)\cong\mathbb{Q}\times\mathbb{Q}$

Published on 03 Jun 2023 - 6:46

score 105 · Answer 4 · 2026-03-26 09:19:55

105

Views

Isomorphism between $R/P$ and $R_P/PR_P$

Published on 26 Mar 2026 - 9:19

score 99 · Answer 5 · 2023-06-14 16:43:12

99

Views

Isomorphism between quotient polynomial rings

Published on 14 Jun 2023 - 16:43

score 57 · Answer 6 · 2023-07-07 12:16:07

57

Views

Decomposition of the field of Laurent formal power series in a polynomial ring and a formal power series ring

Published on 07 Jul 2023 - 12:16

score 77 · Answer 7 · 2023-09-04 02:25:15

77

Views

Prove that $\mathbb{Q}[x]/\langle 3+3x+x^2\rangle \cong \mathbb{Q}(i\sqrt{3})$

Published on 04 Sep 2023 - 2:25

score 37 · Answer 8 · 2023-09-10 18:50:50

37

Views

On quotients of subset rings over infinite sets

Published on 10 Sep 2023 - 18:50

score 40 · Answer 9 · 2023-09-26 10:59:56

40

Views

Isomorphism between quotients of two variable formal power series ring

Published on 26 Sep 2023 - 10:59

score 52 · Answer 10 · 2023-09-29 17:01:18

52

Views

Testing isomorphism of simple field extensions

Published on 29 Sep 2023 - 17:01

score 840 · Answer 11 · 2023-10-04 09:00:47

840

Views

Can two fields which are extensions of one another be non isomorphic

Published on 04 Oct 2023 - 9:00

score 74 · Answer 12 · 2023-10-05 03:00:07

74

Views

Show that $\mathbb Z_{(p)} / J(\mathbb Z_{(p)}) \cong \mathbb Z_p$

Published on 05 Oct 2023 - 3:00

score 42 · Answer 13 · 2023-10-15 18:53:59

42

Views

Does the ring homomorphism $f: R_1 → R_2$ mentioned in the First Isomorphism Theorem have to be a bijection?

Published on 15 Oct 2023 - 18:53

score 20 · Answer 14 · 2026-03-25 23:13:04

20

Views

How do we show $F_2[x]/(x^2 + x) ≅ F_2[x]/(x) × F_2[x]/(x + 1) ≅ F_2 × F_2$?

Published on 25 Mar 2026 - 23:13

score 113 · Answer 15 · 2023-10-23 01:22:25

113

Views

If $A \simeq A_1 \times A_2 \times \cdots \times A_k$, show that $M_n(A) \simeq M_n(A_1) \times M_n(A_2) \times \cdots \times M_n(A_k)$

Published on 23 Oct 2023 - 1:22

List Question

What is the monoid ring $K[(\Bbb{N}, \text{lcm})]$ isomorphic to?

Do isomorphisms of quotients of polynomial rings by monomial ideal preserve the constants?

show $\mathbb{Q}[t]/(t^2-1)\cong\mathbb{Q}\times\mathbb{Q}$

Isomorphism between $R/P$ and $R_P/PR_P$

Isomorphism between quotient polynomial rings

Decomposition of the field of Laurent formal power series in a polynomial ring and a formal power series ring

Prove that $\mathbb{Q}[x]/\langle 3+3x+x^2\rangle \cong \mathbb{Q}(i\sqrt{3})$

On quotients of subset rings over infinite sets

Isomorphism between quotients of two variable formal power series ring

Testing isomorphism of simple field extensions

Can two fields which are extensions of one another be non isomorphic

Show that $\mathbb Z_{(p)} / J(\mathbb Z_{(p)}) \cong \mathbb Z_p$

Does the ring homomorphism $f: R_1 → R_2$ mentioned in the First Isomorphism Theorem have to be a bijection?

How do we show $F_2[x]/(x^2 + x) ≅ F_2[x]/(x) × F_2[x]/(x + 1) ≅ F_2 × F_2$?

If $A \simeq A_1 \times A_2 \times \cdots \times A_k$, show that $M_n(A) \simeq M_n(A_1) \times M_n(A_2) \times \cdots \times M_n(A_k)$

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