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Is the splitting field of $x^7+x^5+x^2+1$ over the field $F$ with 25 elements a separable extension?

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#polynomials #ring-theory #roots #splitting-field #separable-extension
89
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Can someone please explain this terminology?

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#abstract-algebra #polynomials #ring-theory #quotient-spaces
461
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Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.

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#abstract-algebra #ring-theory #maximal-and-prime-ideals
259
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gcd of $f(x)$ and 0 polynomial

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#abstract-algebra #ring-theory #gcd-and-lcm #polynomial-rings
63
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How to prove $(s/t)\left(m/u+m'/u'\right)=(s/t)(m/u)+(s/t)(m'/u').$?

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#ring-theory #modules #fractions
61
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Is the concept of a basis of a module over a ring meaningful if unity is not assumed?

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#abstract-algebra #ring-theory #modules #free-modules
136
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Faithfully exact base-change and split extensions

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#ring-theory #modules #homological-algebra #noncommutative-algebra
152
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Irreducible polynomial in $k[x,y,z]$.

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#ring-theory #field-theory #irreducible-polynomials
683
Views

Matrix with Rings and Fields

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#abstract-algebra #ring-theory
42
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Integral ring homomorphisms exercise

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#abstract-algebra #ring-theory #commutative-algebra #ring-homomorphism
216
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Prove that $\varphi$ is a surjective ring homomorphism.

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#abstract-algebra #ring-theory #ring-homomorphism
190
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Maps between Spec of polynomial rings open and closed

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#abstract-algebra #ring-theory #noetherian
69
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Let $K$ be an algebraic number field. Prove that $O_K$ contains infinitely many prime ideals.

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#abstract-algebra #number-theory #ring-theory #algebraic-number-theory #dedekind-domain
68
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Yes/No Is $\frac{ \mathbb{Q}[x] }{<x+2>}$ is Field?

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#abstract-algebra #ring-theory
210
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If $M_c$ is finitely generated, then it is a principal ideal.

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#abstract-algebra #ring-theory #commutative-algebra

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