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How many distinct roots within an algebraic closure

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#abstract-algebra #polynomials #field-theory #finite-fields #irreducible-polynomials
131
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How to define $\mathrm{GF}(2)$ with elements $\{+1,-1\}$?

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#finite-fields
62
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Representation of elements in finite principal ideal local rings

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#abstract-algebra #number-theory #finite-fields
962
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Degree of a splitting field over finite field

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#abstract-algebra #galois-theory #finite-fields #extension-field
290
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Special subspace in vector space over $\mathbb F_5$

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#linear-algebra #vector-spaces #finite-fields #combinatorial-designs
4.8k
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A cubic polynomial over a field is irreducible if it has no roots

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#abstract-algebra #polynomials #finite-fields #irreducible-polynomials
845
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Order of matrix and monic irreducible polynomial over finite field

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#matrices #finite-fields #group-isomorphism
33
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Counting elements of $\Bbb{Z}/2\Bbb{Z}(\alpha)$

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#field-theory #finite-fields
105
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Upper bounds for the number of roots of polynomials, over finite fields, lying in given extensions

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#abstract-algebra #polynomials #roots #finite-fields #analytic-number-theory
2k
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check whether $\mathbb{Z}[x]/(x-3)$ is a field or not?

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#abstract-algebra #finite-fields
51
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Prove that if $\mathbb{F}_{p^n} \subseteq \mathbb{F}_{p^m}$ then $n \mid m$

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#finite-fields #extension-field
48
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Period of matrix-vector multiplication in vector space over $\mathbb{F}_{p}$

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#linear-algebra #matrices #vector-spaces #eigenvalues-eigenvectors #finite-fields
649
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find the number of distinct arrangements such that all columns are linearly independent

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#linear-algebra #combinatorics #finite-fields
278
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Prove that polynomial doesn't have multiple roots over a splitting field

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#polynomials #finite-fields #splitting-field
2.2k
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Amount of elements in finite vector space.

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#linear-algebra #combinatorics #finite-fields

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