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Question regarding stably free module

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#commutative-algebra #projective-module #free-modules
138
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Dimension of a module

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#linear-algebra #abstract-algebra #modules #free-modules
101
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Prove that $(x_1, y_1)$ and $(x_2, y_2)$ form a basis of $\mathbb Z \oplus \mathbb Z$ iff $x_1y_2 - y_2x_1 = \pm 1$

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#abstract-algebra #free-modules
61
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Is the concept of a basis of a module over a ring meaningful if unity is not assumed?

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#abstract-algebra #ring-theory #modules #free-modules
218
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Show that if $R/A$ is IBN then $R$ is IBN.

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#abstract-algebra #proof-verification #ring-theory #modules #free-modules
395
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Over a PID, every submodule of a free module is free

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#proof-verification #commutative-algebra #principal-ideal-domains #free-modules
728
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Computing index of a submodule over the ring $\mathbb{Z}[\omega]$

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#abstract-algebra #modules #free-modules
202
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Submodule of a free module over a principal ring

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#modules #free-modules
108
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Lifting idempotent endomorphisms of the quotient of a projective module

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#abstract-algebra #modules #representation-theory #projective-module #free-modules
480
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Chain maps between projective complexes are nullhomotopic

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#homological-algebra #homotopy-theory #projective-module #free-modules
405
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Surjective Endomorphism of Finitely Generated Modules.

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#commutative-algebra #modules #free-modules #flatness
126
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Prove that the $R$-module $I \bigoplus I$ is free on the generators $(2 ,1+\sqrt{-5})$ and $(1-\sqrt{-5},2)$.

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#abstract-algebra #ring-theory #commutative-algebra #free-modules
1k
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Sets with the same cardinality generates isomorphic free modules.

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#abstract-algebra #modules #free-modules
116
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How can $\mathbb{R}/\mathbb{Z}$ be a free $\mathbb{R}$-module?

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#free-modules
1.6k
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R is a Noetherian ring, then every finitely generated R-module is finitely presented

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#commutative-algebra #modules #noetherian #finitely-generated #free-modules

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