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Exercise 9, Section 4.2 of Hungerford’s Algebra

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#abstract-algebra #modules #direct-sum #free-modules
37
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F is a free ZG-module implies F is also free as a ZK-module

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#abstract-algebra #modules #free-modules
55
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Understanding homomorphism on tensor product of module

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#abstract-algebra #tensor-products #free-modules
57
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Difference betwen universal properties

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#linear-algebra #abstract-algebra #tensor-products #free-modules #universal-property
77
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Why is the submodule of K[x,y] generated by x and y not a free module?

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#abstract-algebra #modules #free-modules
65
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Theorem 11, Section 4.5 of Hungerford's Algebra

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#abstract-algebra #modules #tensor-products #alternative-proof #free-modules
43
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Hint for a Sequence of Free Modules

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#abstract-algebra #exact-sequence #free-modules
25
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Alternative examples of free modules without the IBN property

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#abstract-algebra #free-modules
11
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let R be local Noetherian. Any finitely generated R-module N st. any short exact sequence with $N$-ending is exact after tensor with R-module is free

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#exact-sequence #noetherian #finitely-generated #free-modules #local-rings
35
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Module Theory, Free Modules, Finitely Generated Modules

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#free-modules
33
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Noether normalization and free modules

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#commutative-algebra #modules #integral-domain #free-modules
2.6k
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Prove that every $\mathbb{Z}/6\mathbb{Z}$-module is projective and injective. Find a $\mathbb{Z}/4\mathbb{Z}$-module that is neither.

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#abstract-algebra #modules #projective-module #injective-module #free-modules
1k
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If a polynomial ring is a free module over some subring, is that subring itself a polynomial ring?

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#abstract-algebra #polynomials #ring-theory #commutative-algebra #free-modules
91
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Any characterization of rings over which submodules of left free modules are free?

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#abstract-algebra #ring-theory #modules #noncommutative-algebra #free-modules
145
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Testing if a submodule is free

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#commutative-algebra #modules #groebner-basis #free-modules

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