Question

How to prove finite abelian group is direct sum of cyclic groups by using matrices over Euclidean domain?

score 813 · Answer 1 · 2026-04-11 10:29:51

813

Views

How to prove finite abelian group is direct sum of cyclic groups by using matrices over Euclidean domain?

Published on 11 Apr 2026 - 10:29

score 112 · Answer 2 · 2026-04-10 16:05:55

112

Views

How to use norms to prove non-UFD?

Published on 10 Apr 2026 - 16:05

score 462 · Answer 3 · 2019-08-04 11:57:45

462

Views

characteristic of ring

Published on 04 Aug 2019 - 11:57

score 1k · Answer 4 · 2026-03-25 06:13:00

1k

Views

$V(I)$ consists of a finite set of points if and only $k[x_1,\ldots,x_n]/I$ has Krull dimension zero

Published on 25 Mar 2026 - 6:13

score 71 · Answer 5 · 2019-08-05 02:52:45

71

Views

$a$ is prime in $R$ if and only if $a \bar a $ is prime in $\mathbb{Z}$

Published on 05 Aug 2019 - 2:52

score 128 · Answer 6 · 2026-04-11 13:04:58

128

Views

Generating Ring from its Group of Units

Published on 11 Apr 2026 - 13:04

score 70 · Answer 7 · 2026-03-31 20:21:13

70

Views

Finite ring ideal

Published on 31 Mar 2026 - 20:21

score 153 · Answer 8 · 2026-04-08 19:46:32

153

Views

Unique representations in quadratic integer rings $\mathbb{Z}[\omega]$

Published on 08 Apr 2026 - 19:46

score 1k · Answer 9 · 2026-03-25 23:42:26

1k

Views

The field of fractions of $\mathbb{Z}[[X]]$ and $\mathbb{Q}[[X]]$, the power series rings, are different.

Published on 25 Mar 2026 - 23:42

score 513 · Answer 10 · 2026-03-25 13:56:26

513

Views

If an element has prime norm in the ring of quadratic integers, then it is a prime element

Published on 25 Mar 2026 - 13:56

score 281 · Answer 11 · 2026-04-11 04:07:53

281

Views

Differences in tensor products under change of ring

Published on 11 Apr 2026 - 4:07

score 49 · Answer 12 · 2026-03-31 20:29:11

49

Views

Prove that $ I_{R} (A) $ is the "biggest" subring in $R$ in which $A$ is ideal.

Published on 31 Mar 2026 - 20:29

score 124 · Answer 13 · 2019-08-06 08:58:21

124

Views

Why is $I^j I^k\subseteq I^{j+k}$ if $I$ is an ideal of a commutative ring $R$?

Published on 06 Aug 2019 - 8:58

score 76 · Answer 14 · 2026-04-11 17:38:46

76

Views

Prove that in ring $\mathbb{Z}, \forall a,b \in \mathbb{Z} $, $(a,b) = (d)$, where $ d = \mathrm{gcd}(a,b)$

Published on 11 Apr 2026 - 17:38

score 132 · Answer 15 · 2026-03-29 18:51:04

132

Views

Find a ring $R$ with a chain of prime ideals of length 2008.

Published on 29 Mar 2026 - 18:51

List Question

How to prove finite abelian group is direct sum of cyclic groups by using matrices over Euclidean domain?

How to use norms to prove non-UFD?

characteristic of ring

$V(I)$ consists of a finite set of points if and only $k[x_1,\ldots,x_n]/I$ has Krull dimension zero

$a$ is prime in $R$ if and only if $a \bar a $ is prime in $\mathbb{Z}$

Generating Ring from its Group of Units

Finite ring ideal

Unique representations in quadratic integer rings $\mathbb{Z}[\omega]$

The field of fractions of $\mathbb{Z}[[X]]$ and $\mathbb{Q}[[X]]$, the power series rings, are different.

If an element has prime norm in the ring of quadratic integers, then it is a prime element

Differences in tensor products under change of ring

Prove that $ I_{R} (A) $ is the "biggest" subring in $R$ in which $A$ is ideal.

Why is $I^j I^k\subseteq I^{j+k}$ if $I$ is an ideal of a commutative ring $R$?

Prove that in ring $\mathbb{Z}, \forall a,b \in \mathbb{Z} $, $(a,b) = (d)$, where $ d = \mathrm{gcd}(a,b)$

Find a ring $R$ with a chain of prime ideals of length 2008.

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