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Let $x$ be a quaternion of norm $1$, then $x=[1+\overline{x},y]$ for some $y\in\mathbb{H}^*$

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#abstract-algebra #group-theory #quaternions
44
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Show $A_n$ is invariant under conjugation $\pi \in S_n , \pi A_n \pi^{-1} =A_n $

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#abstract-algebra
121
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Factor of the product of rings cannot be free module?

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#abstract-algebra #modules #free-modules
170
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Inverse of The Element of Ring

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#abstract-algebra #ring-theory
154
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Existence of hollow ideal in commutative rings

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#abstract-algebra #ring-theory #commutative-algebra
262
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how to prove homomorphism

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#abstract-algebra #group-theory #finite-groups #permutations #symmetric-groups
539
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Galois group of $x^{4}-4x^{2}+5$ over $\mathbb{Q}$.

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#abstract-algebra
1.7k
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If there exists a subgroup of index 2, show that any element squared is in the subgroup.

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#abstract-algebra
3k
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Find all the subrings of $Z_{12}$ and if they have a multiplicative identity

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#abstract-algebra #elementary-number-theory #ring-theory
44
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Eigenvalues of differentiable paths

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#linear-algebra #abstract-algebra #differential-geometry #algebraic-geometry #eigenvalues-eigenvectors
990
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Galois group of $x^n+1$ over $\Bbb Q$

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#abstract-algebra #galois-theory #splitting-field #cyclotomic-fields
85
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How come only irreducible polynomials are considered when talking about field extensions?

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#abstract-algebra #field-theory
1k
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Dual of the symmetric algebra of the dual

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#linear-algebra #abstract-algebra #vector-spaces
1.7k
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Counting irreducible polynomials over finite fields

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#abstract-algebra #ring-theory #polynomial-rings
64
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Notation in algebra

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#abstract-algebra #vector-spaces #notation

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