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New posts in positive-characteristic
Characteristic of a finite ring with $34$ units
abstract-algebra
commutative-algebra
ring-theory
totient-function
positive-characteristic
Determinant of Killing form of sl_n
linear-algebra
determinant
lie-algebras
positive-characteristic
Let $\alpha$ be a root of $(x^2-a)$ and $\beta$ be a root of $(x^2-b)$. Provide conditions over $a$ and $b$ to have $F=K(\alpha+\beta)$.
abstract-algebra
field-theory
splitting-field
positive-characteristic
Show that $f(x) = x^p -x -1 \in \Bbb{F}_p[x]$ is irreducible over $\Bbb{F}_p$ for every $p$.
abstract-algebra
field-theory
finite-fields
positive-characteristic
Problem in Jacobson's Basic Algebra (Vol. I)
abstract-algebra
field-theory
finite-fields
positive-characteristic
Prove that a polynomial is irreducible or the field contains a $p$th root
abstract-algebra
field-theory
irreducible-polynomials
positive-characteristic
Can a "generalized field" with three operations be infinite? [duplicate]
field-theory
group-isomorphism
positive-characteristic
Example of ring can’t be defined over finite field.
abstract-algebra
ring-theory
finite-fields
positive-characteristic
How can a field have a finite characteristic $p$, given that a field has no zero divisors?
abstract-algebra
field-theory
positive-characteristic
Does there exist a pair of infinite fields, the additive group of one isomorphic to the multiplicative group of the other?
field-theory
group-isomorphism
positive-characteristic
Can a ring of positive characteristic have infinite number of elements?
abstract-algebra
ring-theory
positive-characteristic
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
positive-characteristic
abstract-algebra
polynomials
field-theory
irreducible-polynomials
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