Question

Does sufficient information on the multiplicative group of the fraction field of a GCD and Factorization domain, captures unique factorization?

score 55 · Answer 1 · 2026-03-25 01:18:20

55

Views

Does sufficient information on the multiplicative group of the fraction field of a GCD and Factorization domain, captures unique factorization?

Published on 25 Mar 2026 - 1:18

score 231 · Answer 2 · 2026-03-25 14:25:34

231

Views

Can $G/2G$ and $\mathbb Z / 2\mathbb Z \times ... \times \mathbb Z / 2\mathbb Z$ be not isomorphic? $G$ is a free abelian group with finite basis.

Published on 25 Mar 2026 - 14:25

score 209 · Answer 3 · 2026-03-25 05:09:44

209

Views

Clarification on what is and is not a free abelian group

Published on 25 Mar 2026 - 5:09

score 226 · Answer 4 · 2026-03-25 05:11:19

226

Views

Alternative definition on free modules.

Published on 25 Mar 2026 - 5:11

score 50 · Answer 5 · 2026-03-22 11:27:07

50

Views

How prove a group is not free abelian group

Published on 22 Mar 2026 - 11:27

score 152 · Answer 6 · 2026-03-25 14:25:54

152

Views

Is studying a free group (or other free object) equivalent to considering only the consequences of the basic axioms?

Published on 25 Mar 2026 - 14:25

score 117 · Answer 7 · 2026-03-25 14:25:24

117

Views

Let $A$ be an abelian finitely generated free group and $A/B$ be a torsion group. Show that $rank(A)=rank(B)$.

Published on 25 Mar 2026 - 14:25

score 70 · Answer 8 · 2019-01-30 03:46:16

70

Views

If $G=A\times B$, where $A$- torsion group, $B$-free abelian group, how to show that $A=G_{tor}$

Published on 30 Jan 2019 - 3:46

score 1.7k · Answer 9 · 2026-03-25 19:06:20

1.7k

Views

An abelian group $G$ is free abelian if and only if satisfies the projective property

Published on 25 Mar 2026 - 19:06

score 628 · Answer 10 · 2026-03-22 20:58:19

628

Views

Basis of subgroup of a free abelian group

Published on 22 Mar 2026 - 20:58

score 134 · Answer 11 · 2026-03-25 07:48:41

134

Views

Proving the Free Abelian Group is Free Abelian...?

Published on 25 Mar 2026 - 7:48

score 101 · Answer 12 · 2026-03-25 12:46:17

101

Views

Universal Property...The Map is not Well-defined?

Published on 25 Mar 2026 - 12:46

score 498 · Answer 13 · 2019-04-08 13:09:58

498

Views

how to deduce two matrices $P$ and $Q$ are square if $PQ=I_{n}$ and $QP=I_{m}$

Published on 08 Apr 2019 - 13:09

score 112 · Answer 14 · 2019-04-13 04:57:56

112

Views

How do we show two functions have orthogonal actions on a set or group?

Published on 13 Apr 2019 - 4:57

score 427 · Answer 15 · 2019-04-20 17:59:13

427

Views

Direct sum of $n$ (infinite) cyclic groups isomorphic to direct sum of $n$ copies of $\mathbb{Z}$?

Published on 20 Apr 2019 - 17:59

List Question

Does sufficient information on the multiplicative group of the fraction field of a GCD and Factorization domain, captures unique factorization?

Can $G/2G$ and $\mathbb Z / 2\mathbb Z \times ... \times \mathbb Z / 2\mathbb Z$ be not isomorphic? $G$ is a free abelian group with finite basis.

Clarification on what is and is not a free abelian group

Alternative definition on free modules.

How prove a group is not free abelian group

Is studying a free group (or other free object) equivalent to considering only the consequences of the basic axioms?

Let $A$ be an abelian finitely generated free group and $A/B$ be a torsion group. Show that $rank(A)=rank(B)$.

If $G=A\times B$, where $A$- torsion group, $B$-free abelian group, how to show that $A=G_{tor}$

An abelian group $G$ is free abelian if and only if satisfies the projective property

Basis of subgroup of a free abelian group

Proving the Free Abelian Group is Free Abelian...?

Universal Property...The Map is not Well-defined?

how to deduce two matrices $P$ and $Q$ are square if $PQ=I_{n}$ and $QP=I_{m}$

How do we show two functions have orthogonal actions on a set or group?

Direct sum of $n$ (infinite) cyclic groups isomorphic to direct sum of $n$ copies of $\mathbb{Z}$?

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