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Proving a module is projective.

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#abstract-algebra #modules #projective-module
30
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Proving a specific module is projective.

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#abstract-algebra #modules #projective-module
471
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Inverse of $1+\theta$?

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#abstract-algebra #field-theory
100
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Quotient rings as complements of ideals

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#abstract-algebra #ring-theory #ideals #quotient-group
56
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$A\otimes M \otimes A$ projective as $A^e$-module, where $A$ and $M$ are projective over commutative ring $k$

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#abstract-algebra #modules #homological-algebra
56
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Smallest $n\in \mathbb{Z}_{>0}$ for existence of a monomorphism $G \rightarrow S_n$

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#abstract-algebra #group-theory #permutations #group-isomorphism #group-homomorphism
71
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High-degree pieces of graded ideal with coprime generators

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#abstract-algebra #ring-theory #commutative-algebra #ideals #graded-rings
2.8k
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Proof that a factorization domain is a unique factorization domain if and only if every irreducible element is prime.

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#abstract-algebra #ring-theory #proof-writing
67
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If $a,b,n \in \mathbb{Z}$, & $n \mid (a+b)$, prove $n$ does not necessarily divide $ (a^2+b^2)$

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#abstract-algebra #elementary-number-theory #divisibility #integers
200
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Does $\mathbb Z/{2}\times\mathbb Z/{2}$ have no maximal and prime ideal?

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
70
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Positive element of c*-algebra

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#abstract-algebra
461
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Is $\mathbb{C}[x,y]/(y)$ always isomorphic to $\mathbb{C}[x]$

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#abstract-algebra #ring-theory
57
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finding a bijective map from $ F(m,n)\times F(k,n)$ to $F(m+k,n)$

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#abstract-algebra #functional-analysis #functions #hilbert-spaces #inverse
259
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Homomorphisms of group $\mathbb{Z}$ to itself send even integers to even integers

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#abstract-algebra #integers
828
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Determine kernel of localization map of ring

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#abstract-algebra #ring-theory #commutative-algebra #localization

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