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Generalized Notion of Krylov Subspaces

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#linear-algebra #abstract-algebra #vector-spaces #modules #free-modules
84
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Construction of the free operad

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#combinatorics #algebraic-topology #category-theory #free-modules #operads
33
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partial Quillen-Suslin on square matrix

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#abstract-algebra #algebraic-geometry #projective-module #free-modules
116
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Why a nonzero finite abelian group is not projective?

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#abstract-algebra #modules #exact-sequence #projective-module #free-modules
81
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Prove that the polynomial ring $R[x]$ is a flat $R$-module.

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#abstract-algebra #ring-theory #modules #free-modules #flatness
84
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Proving two modules are free based on their direct sum

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#commutative-algebra #modules #direct-sum #free-modules #local-rings
51
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Finitely generated $R$-module has a free resolution of length at most $1$?

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#abstract-algebra #homological-algebra #free-modules
58
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Generating set for submodule of free module over a PIR

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#abstract-algebra #ring-theory #modules #finitely-generated #free-modules
76
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Showing that the rank of $M$ is exactly $1.$

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#abstract-algebra #vector-spaces #modules #free-modules
54
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Free submodules of an integral $R.$

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#abstract-algebra #ideals #principal-ideal-domains #integral-domain #free-modules
24
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Polynomial rings and symmetric algebras on the dual module are isomorphic

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#polynomials #free-modules #symmetric-algebra
14
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Bundle map from $Spec(R[x_{1}, \dots, x_{n}])$ to $Spec(R)$

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#spectral-theory #vector-bundles #free-modules
122
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Theorem 4, Section 4.2 of Hungerford’s Algebra

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#abstract-algebra #vector-spaces #proof-explanation #modules #free-modules
114
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Lemma 10, Section 4.2 of Hungerford’s Algebra

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#abstract-algebra #proof-explanation #modules #free-modules
103
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Projective and free modules

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#commutative-algebra #modules #projective-module #free-modules #graded-rings

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