Question

Is there a way of proving that $\mathbb{Z}[i]$ and $\mathbb{Z}[\sqrt{-2}]$ are UFD s without showing that they are euclidian domains?

score 370 · Answer 1 · 2026-04-29 12:44:27

370

Views

Is there a way of proving that $\mathbb{Z}[i]$ and $\mathbb{Z}[\sqrt{-2}]$ are UFD s without showing that they are euclidian domains?

Published on 29 Apr 2026 - 12:44

score 79 · Answer 2 · 2026-04-14 10:41:01

79

Views

Sum of two minimal direct summands

Published on 14 Apr 2026 - 10:41

score 62 · Answer 3 · 2026-04-12 07:27:31

62

Views

Constructing First Order Logic sentence to describe a difference between $\mathbb{Z}$ and $\mathbb{C}$

Published on 12 Apr 2026 - 7:27

score 180 · Answer 4 · 2026-04-14 19:49:54

180

Views

True or False: Let A $\supseteq$ R be an integral ring extension of R, with A being a domain...

Published on 14 Apr 2026 - 19:49

score 161 · Answer 5 · 2026-04-16 05:26:34

161

Views

If |G/H|=4 then G is union of three proper subgroups

Published on 16 Apr 2026 - 5:26

score 173 · Answer 6 · 2026-04-25 15:21:25

173

Views

A non co-hopfian simple group?

Published on 25 Apr 2026 - 15:21

score 359 · Answer 7 · 2026-05-03 04:36:38

359

Views

Is there a name for an algebraic structure with only "addition" and "truncated subtraction"?

Published on 03 May 2026 - 4:36

score 54 · Answer 8 · 2026-04-16 20:47:51

54

Views

Determine the permutation matrix of a permutation in $S_{n}$

Published on 16 Apr 2026 - 20:47

score 68 · Answer 9 · 2026-05-02 05:18:32

68

Views

How to construction a division ring from the given field?

Published on 02 May 2026 - 5:18

score 53 · Answer 10 · 2026-04-16 13:33:12

53

Views

Describe the splitting field $F$ of the polynomial $f=x^4+x^2+1$ over $\mathbb{Q}$

Published on 16 Apr 2026 - 13:33

score 46 · Answer 11 · 2026-04-15 18:20:19

46

Views

degree of quotient $K[X]/P_{\alpha}$

Published on 15 Apr 2026 - 18:20

score 100 · Answer 12 · 2026-04-30 12:36:59

100

Views

Uniqueness of two side zeroes of binary operation

Published on 30 Apr 2026 - 12:36

score 69 · Answer 13 · 2026-04-11 08:58:21

69

Views

Homomorphism theorem - Why is a normal subgroup needed

Published on 11 Apr 2026 - 8:58

score 527 · Answer 14 · 2026-05-05 04:12:00

527

Views

Question about a proof of $\mathbb{Z}[i]/(2+i)\cong \mathbb{Z}/5\mathbb{Z}$

Published on 05 May 2026 - 4:12

score 192 · Answer 15 · 2026-04-15 12:43:27

192

Views

"Dimension inequality" preserving linear map for vector spaces

Published on 15 Apr 2026 - 12:43

List Question

Is there a way of proving that $\mathbb{Z}[i]$ and $\mathbb{Z}[\sqrt{-2}]$ are UFD s without showing that they are euclidian domains?

Sum of two minimal direct summands

Constructing First Order Logic sentence to describe a difference between $\mathbb{Z}$ and $\mathbb{C}$

True or False: Let A $\supseteq$ R be an integral ring extension of R, with A being a domain...

If |G/H|=4 then G is union of three proper subgroups

A non co-hopfian simple group?

Is there a name for an algebraic structure with only "addition" and "truncated subtraction"?

Determine the permutation matrix of a permutation in $S_{n}$

How to construction a division ring from the given field?

Describe the splitting field $F$ of the polynomial $f=x^4+x^2+1$ over $\mathbb{Q}$

degree of quotient $K[X]/P_{\alpha}$

Uniqueness of two side zeroes of binary operation

Homomorphism theorem - Why is a normal subgroup needed

Question about a proof of $\mathbb{Z}[i]/(2+i)\cong \mathbb{Z}/5\mathbb{Z}$

"Dimension inequality" preserving linear map for vector spaces

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