List questions from free-modules

Published on 26 Mar 2026 - 21:26

165

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Basis for a free abelian group of finite rank

Published on 22 Nov 2017 - 5:13

237

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If $R$ is a finitely generated $D$-algebra, $D$ a division ring, then $R$ has finite basis over $D$?

Published on 23 Feb 2026 - 8:25

1.6k

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Submodule of a free module

Published on 30 Nov 2017 - 11:50

134

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Need a help in understanding Theorem 2.4 in section 2, chapter 4 of Hungerford Algebra.

Published on 01 Dec 2017 - 11:34

203

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Free modules over a PID

Published on 03 Dec 2017 - 15:01

107

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$V$ becoming a $K[x]$-module w.r.t this addition and scalar multiplication

Published on 10 Dec 2017 - 10:39

1.5k

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Rational canonical form of diagonal matrix

Published on 16 Dec 2017 - 0:53

140

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Counterexample to $M$ a $R$-module or rank $n$ then if $N\leq M$, $N$ is a $R$-module of rank $\leq n$

Published on 03 Jan 2018 - 2:34

2.5k

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Every $R$-module is a quotient of a free module

Published on 10 Jan 2018 - 16:52

327

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In the proof of every free R-module is projective, where do we use being free?

Published on 12 Jan 2018 - 17:41

1k

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Every set of $n$ generators is a basis for $A^{n}$

Published on 15 Jul 2011 - 20:29

1.8k

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Is there any relation of injective modules to free modules?

Published on 27 Mar 2026 - 15:07

5.5k

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A surjective homomorphism between finite free modules of the same rank

Published on 03 Jun 2012 - 22:59

1.5k

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Generators of a finitely generated free module over a commutative ring

Published on 20 Nov 2012 - 15:28

List Question

$\kappa$-free abelian groups and inaccessible cardinals

Basis for a free abelian group of finite rank

If $R$ is a finitely generated $D$-algebra, $D$ a division ring, then $R$ has finite basis over $D$?

Submodule of a free module

Need a help in understanding Theorem 2.4 in section 2, chapter 4 of Hungerford Algebra.

Free modules over a PID

$V$ becoming a $K[x]$-module w.r.t this addition and scalar multiplication

Rational canonical form of diagonal matrix

Counterexample to $M$ a $R$-module or rank $n$ then if $N\leq M$, $N$ is a $R$-module of rank $\leq n$

Every $R$-module is a quotient of a free module

In the proof of every free R-module is projective, where do we use being free?

Every set of $n$ generators is a basis for $A^{n}$

Is there any relation of injective modules to free modules?

A surjective homomorphism between finite free modules of the same rank

Generators of a finitely generated free module over a commutative ring

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