Newbetuts
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New posts in field-theory
Show that $\beta $ is algebraic over $F(\alpha)$.
abstract-algebra
field-theory
Polynomials such that $\frac{P(x^2)}{P(x)}$ is also a polynomial [duplicate]
abstract-algebra
polynomials
field-theory
irreducible-polynomials
Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
linear-algebra
matrices
field-theory
matrix-equations
What is the main difference between a vector space and a field?
vector-spaces
field-theory
If the field of a vector space weren't characteristic zero, then what would change in the theory?
linear-algebra
matrices
vector-spaces
field-theory
linear-transformations
Is $\{0\}$ a field?
field-theory
axioms
A freshman's dream
field-theory
finite-fields
alternative-proof
Intermediate ring between a field and an algebraic extension.
abstract-algebra
field-theory
Why must a field whose a group of units is cyclic be finite?
abstract-algebra
group-theory
field-theory
finite-fields
cyclic-groups
How to transform a general higher degree five or higher equation to normal form?
field-theory
galois-theory
elliptic-functions
A sufficient and necessary condition for $\mathbb{C}(f(x),g(x))=\mathbb{C}(x)$?
algebraic-geometry
polynomials
field-theory
function-fields
Subfields of finite fields
field-theory
finite-fields
Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
abstract-algebra
group-theory
polynomials
field-theory
galois-theory
When are nonintersecting finite degree field extensions linearly disjoint?
field-theory
Do the rings $\mathbb{Z}[x]$ or $\mathbb{Q}[x]$ have a quotient isomorphic to the field with 9 elements?
abstract-algebra
field-theory
ideals
finite-fields
maximal-and-prime-ideals
Suppose that $c$ is transcendental over $\mathbb{Q}.$ Show that $\sqrt{c}$ and $c + \sqrt{c}$ are also transcendental.
abstract-algebra
polynomials
field-theory
transcendental-numbers
Intersection of two subfields of the Rational Function Field in characteristic $0$
abstract-algebra
field-theory
galois-theory
How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$? [duplicate]
abstract-algebra
polynomials
field-theory
finite-fields
irreducible-polynomials
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
abstract-algebra
field-theory
galois-theory
Is the minimal polynomial also minimal over the closure of the base field? [closed]
linear-algebra
field-theory
minimal-polynomials
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