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Exact sequence construction

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#abstract-algebra #modules #free-modules
66
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Example of both finitely and infinitely generated free modules which are direct sum of two non free modules

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#abstract-algebra #modules #free-modules
304
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Unique representation of zero in terms of the basis of a free module

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#abstract-algebra #vector-spaces #free-modules
529
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The exact sequence of tensor product

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#modules #tensor-products #exact-sequence #free-modules
473
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Proof explanation: Every module is the quotient of free module

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#abstract-algebra #commutative-algebra #proof-explanation #free-modules
482
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Is a finitely generated torsion-free R-module free over R if R is an integral domain?

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#abstract-algebra #field-theory #modules #free-modules
2k
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Pullback of locally free sheaves is locally free

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#algebraic-geometry #sheaf-theory #schemes #coherent-sheaves #free-modules
215
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Basis of a free module under module homomorphisms

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#abstract-algebra #free-modules
394
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Linear independence for modules over a zero ring

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#linear-algebra #abstract-algebra #modules #free-modules
116
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Modules $(K\otimes A)\otimes_{K}\left(K\otimes B\right)$ and $K\otimes(A\otimes B)$ isomorphic?

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#modules #tensor-products #free-modules
905
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Determinant for a basis of a free module

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#linear-algebra #abstract-algebra #determinant #change-of-basis #free-modules
106
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$\Bbb R$-algebras of rank $1$

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#abstract-algebra #modules #free-modules
100
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What do the finitely generated free $R$-modules look like?

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#abstract-algebra #ring-theory #modules #free-modules
1.3k
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Why is every vector space free, but not every module?

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#vector-spaces #modules #free-modules
88
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I don't understand a step in the statement of the structure theorem of finitely generated modules over a PID

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#modules #principal-ideal-domains #free-modules

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