List questions from field-theory

Published on 17 Apr 2026 - 5:52

216

Views

How to show that $[\mathbb Q(\sqrt[3]2,\sqrt[3]5,i\sqrt 3):\mathbb Q(i\sqrt 3)]=9$

Published on 18 Apr 2026 - 6:45

175

Views

Is there a faster way to factor $X^{12}-1$ over $\mathbb{F}_5[X]$?

Published on 14 Apr 2026 - 2:34

869

Views

Find the field of fractions and the integral closure of a subring of $\mathbb Z[x]$.

Published on 11 Apr 2026 - 19:24

53

Views

Find the cardinality of $\mathbb{F}_2$ adjoin a root of $X^4 + X + 1$

Published on 16 Apr 2026 - 5:34

620

Views

Field of polynomials mod n?

Published on 14 Apr 2026 - 0:24

104

Views

Finite Ring with unity and no zero divisors is field

Published on 13 Apr 2026 - 17:32

59

Views

If $K$ is a field with an infinite number of elements and $f(x),g(x)\in K[x]$ such that for $\forall \alpha\in K$ $f(\alpha)=g(\alpha)$, then $f=g$

Published on 15 Apr 2026 - 14:49

199

Views

Finding irreducible polynomial which is not separable.

Published on 09 Apr 2026 - 13:38

65

Views

$K[T]/(f(T))\simeq F[T]/(f(T))\Rightarrow K\simeq F$

Published on 16 Apr 2026 - 16:57

36

Views

Reducing $x^{p-1}$ mod $p$

Published on 16 Apr 2026 - 7:54

842

Views

How to prove that a maximal ideal of a ring is unique?

Published on 11 Apr 2026 - 8:17

339

Views

If $\alpha,\beta\in L$ algebraic over $K$ with degrees $m,n$, then $\alpha\pm\beta$ is algebraic with degree $\leq mn$

Published on 14 Apr 2026 - 20:56

127

Views

Extension field with roots of unity(Basis and generator of the field As the vector space)

Published on 15 Apr 2026 - 14:42

57

Views

Show that $Q(cos(40°))$ a normal extension of $Q$

Published on 14 Apr 2026 - 22:29

List Question

Where do the coefficients belong to?

How to show that $[\mathbb Q(\sqrt[3]2,\sqrt[3]5,i\sqrt 3):\mathbb Q(i\sqrt 3)]=9$

Is there a faster way to factor $X^{12}-1$ over $\mathbb{F}_5[X]$?

Find the field of fractions and the integral closure of a subring of $\mathbb Z[x]$.

Find the cardinality of $\mathbb{F}_2$ adjoin a root of $X^4 + X + 1$

Field of polynomials mod n?

Finite Ring with unity and no zero divisors is field

If $K$ is a field with an infinite number of elements and $f(x),g(x)\in K[x]$ such that for $\forall \alpha\in K$ $f(\alpha)=g(\alpha)$, then $f=g$

Finding irreducible polynomial which is not separable.

$K[T]/(f(T))\simeq F[T]/(f(T))\Rightarrow K\simeq F$

Reducing $x^{p-1}$ mod $p$

How to prove that a maximal ideal of a ring is unique?

If $\alpha,\beta\in L$ algebraic over $K$ with degrees $m,n$, then $\alpha\pm\beta$ is algebraic with degree $\leq mn$

Extension field with roots of unity(Basis and generator of the field As the vector space)

Show that $Q(cos(40°))$ a normal extension of $Q$

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