Question

Is there a functor $F$ preserving finite direct sums but not split exact sequences, for which $F\mathbb{Z}$ is free and finitely generated?

score 171 · Answer 1 · 2026-03-25 23:58:45

171

Views

Is there a functor $F$ preserving finite direct sums but not split exact sequences, for which $F\mathbb{Z}$ is free and finitely generated?

Published on 25 Mar 2026 - 23:58

score 319 · Answer 2 · 2020-04-12 15:05:41

319

Views

Duality for free abelian groups and for finite abelian groups

Published on 12 Apr 2020 - 15:05

score 65 · Answer 3 · 2026-03-25 23:53:07

65

Views

Does a functor which is additive by arbitrary isomorphism restrict and corestrict to an actually additive functor?

Published on 25 Mar 2026 - 23:53

score 68 · Answer 4 · 2020-04-16 15:00:42

68

Views

Lattice structure of free abelian group on a set $X$

Published on 16 Apr 2020 - 15:00

score 140 · Answer 5 · 2026-02-23 02:42:08

140

Views

Does the Unique Product Property mean that there are only two elements in the set that can create any other in the set, given an operation?

Published on 23 Feb 2026 - 2:42

score 46 · Answer 6 · 2026-03-25 21:22:57

46

Views

Quotient of $\mathbb{Z} \times \mathbb{Z}$ by subgroup generated by $(n,m)$.

Published on 25 Mar 2026 - 21:22

score 154 · Answer 7 · 2020-06-08 11:25:05

154

Views

Free abelian group - exercise

Published on 08 Jun 2020 - 11:25

score 58 · Answer 8 · 2020-06-19 20:07:25

58

Views

Determine what the automorphism group of $\Bbb Z_{7^3}$ looks like.

Published on 19 Jun 2020 - 20:07

score 98 · Answer 9 · 2020-06-19 20:50:30

98

Views

Prove that $A/B$ is cyclic if and only if $\gcd(a,b,c,d) = 1$.

Published on 19 Jun 2020 - 20:50

score 135 · Answer 10 · 2020-06-22 17:14:56

135

Views

The existence of group isomorphism between Euclidean space.

Published on 22 Jun 2020 - 17:14

score 113 · Answer 11 · 2020-06-22 19:56:24

113

Views

A free abelian group and a free group quotient by its commutator group

Published on 22 Jun 2020 - 19:56

score 337 · Answer 12 · 2016-09-02 12:59:35

337

Views

Let $S$ be a generating subset of a free abelian group of rank $k$ s.t. $|S|=k$ , then is the set $S$ linearly independent?

Published on 02 Sep 2016 - 12:59

score 211 · Answer 13 · 2016-09-02 13:08:58

211

Views

$G$ be a free abelian group of rank $k$ , let $S$ be a subset of $G$ that generates $G$ then is it true that $|S| \ge k$?

Published on 02 Sep 2016 - 13:08

score 37 · Answer 14 · 2016-09-02 16:18:11

37

Views

$G$ be a free abelian group of rank $k$ , let $S$ be a subset of $G$ linearly independent over $\mathbb Z$ , then is it true that $|S| \le k$?

Published on 02 Sep 2016 - 16:18

score 403 · Answer 15 · 2016-11-09 00:36:54

403

Views

Prove that any subgroup of a free Abelian group of rank $r$ is free Abelian of rank at most $r$.

Published on 09 Nov 2016 - 0:36

List Question

Is there a functor $F$ preserving finite direct sums but not split exact sequences, for which $F\mathbb{Z}$ is free and finitely generated?

Duality for free abelian groups and for finite abelian groups

Does a functor which is additive by arbitrary isomorphism restrict and corestrict to an actually additive functor?

Lattice structure of free abelian group on a set $X$

Does the Unique Product Property mean that there are only two elements in the set that can create any other in the set, given an operation?

Quotient of $\mathbb{Z} \times \mathbb{Z}$ by subgroup generated by $(n,m)$.

Free abelian group - exercise

Determine what the automorphism group of $\Bbb Z_{7^3}$ looks like.

Prove that $A/B$ is cyclic if and only if $\gcd(a,b,c,d) = 1$.

The existence of group isomorphism between Euclidean space.

A free abelian group and a free group quotient by its commutator group

Let $S$ be a generating subset of a free abelian group of rank $k$ s.t. $|S|=k$ , then is the set $S$ linearly independent?

$G$ be a free abelian group of rank $k$ , let $S$ be a subset of $G$ that generates $G$ then is it true that $|S| \ge k$?

$G$ be a free abelian group of rank $k$ , let $S$ be a subset of $G$ linearly independent over $\mathbb Z$ , then is it true that $|S| \le k$?

Prove that any subgroup of a free Abelian group of rank $r$ is free Abelian of rank at most $r$.

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