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Why does this ring have rank $k!$?

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#abstract-algebra #ring-theory #modules #tensor-products
1.7k
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About the definitions of direct product and direct sum of modules.

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#abstract-algebra #modules
1k
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How many solutions of $\mod 63$ : $x^2=1 \pmod7 $ and $x^3=1\pmod 9$

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#modules #congruences
956
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Hom and direct sums 3

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#modules
518
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What is the simplest example of the tame representation type?

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#abstract-algebra #vector-spaces #field-theory #modules #representation-theory
943
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The sum of a family of submodules

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#abstract-algebra #group-theory #modules
1.1k
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Polynomial ring as direct sum of modules

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#abstract-algebra #modules
323
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Proving that a prime ideal $p \subset R$ yields a prime ideal $p[x] \subset R[x]$

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#abstract-algebra #ring-theory #proof-verification #modules #maximal-and-prime-ideals
51
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Application of Structure Theorem to Prove Simultaneous Diagonalizability and Group of Units of Cyclic Groups

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#linear-algebra #elementary-number-theory #modules #principal-ideal-domains
84
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What is number of irreducible characters in modular representation?

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#abstract-algebra #modules #representation-theory #characters
120
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Isomorphic for free modules implies for projective

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#commutative-algebra #modules #projective-module
143
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Question about generators and Hom functor

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#abstract-algebra #group-theory #category-theory #modules #abelian-categories
128
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A question on extension of rings which related to their direct summands

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#abstract-algebra #ring-theory #modules
362
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Help with proving a fact about injective modules

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#abstract-algebra #modules #injective-module
737
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Why not use the Cartesian product for the monoidal category of modules? Why use the tensor product?

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#category-theory #modules #tensor-products #hopf-algebras #monoidal-categories

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