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Dummit and Foote Universal Property of Tensor Products

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#abstract-algebra #modules #tensor-products #universal-property #free-modules
52
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Alternative Definition of Rank

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#linear-algebra #modules #free-modules
207
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Dual module $M^\#$ contains non-torsion element if $M$ does

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#linear-algebra #abstract-algebra #commutative-algebra #modules #free-modules
2.6k
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Free vector space over a set

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#linear-algebra #abstract-algebra #vector-spaces #category-theory #free-modules
554
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Endomorphism between direct sum of modules $M := M_1 \oplus M_2$

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#linear-algebra #abstract-algebra #modules #multilinear-algebra #free-modules
857
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If the direct sum of a module with a free module is free, then that module is zero

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#commutative-algebra #modules #projective-module #free-modules
70
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Direct sum in free modules.

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#abstract-algebra #free-modules
53
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When is the quotient of an algebra by a polynomial algebra a free module?

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#abstract-algebra #symmetric-polynomials #free-modules
181
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$M/PM$ is torsion-free

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#abstract-algebra #commutative-algebra #modules #free-modules
647
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Show that $\ker(\phi)$ is finitely generated

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#abstract-algebra #proof-verification #modules #free-modules
390
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Why does every module over an $R$ conmutative ring is free, if $R$ is a field?

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#field-theory #modules #free-modules
179
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Do we have $R\simeq S$ for two submodules $R,S$ of $A^n$?

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#abstract-algebra #commutative-algebra #modules #free-modules #module-isomorphism
323
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Is $R$ finitely generated?

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#abstract-algebra #commutative-algebra #modules #free-modules #module-isomorphism
427
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Is the "basis" of a free module linearly independent?

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#abstract-algebra #modules #free-modules
990
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Vector space versus Free module

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#abstract-algebra #soft-question #free-modules

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