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15
147
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First Isomorphism Theorem (another)

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#abstract-algebra #ring-theory #field-theory #ring-isomorphism
660
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Let $R=\mathbb Z[x]$ be the ring of polynomials over $\mathbb Z$. Prove that the ideal $(x,p)$ is maximal if and only if $p$ is a prime number.

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#abstract-algebra #ring-theory
65
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Asking about $R$-submodules which are not finitely generated.

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#abstract-algebra #ring-theory #modules
62
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ideals in ring of fractions

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#ring-theory
91
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example of commutative ring where two equal principal ideals have generators which do not differ by a unit

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#abstract-algebra #ring-theory #commutative-algebra #examples-counterexamples
95
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$\mathrm{Hom}_{eAe}(A,N)\cong \mathrm{Hom}_{eAe}(Ae,N)$

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#abstract-algebra #ring-theory #modules #idempotents
105
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Quotient Rings and Homomorphic Images in $\mathscr{F}(\mathbb{R})$

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#abstract-algebra #proof-verification #ring-theory
81
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About minimal ideals and division rings

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#abstract-algebra #ring-theory #ideals
99
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Polynomial x$^3$ - 2 is not the product of two nonconstant polynomials $f$ = $gh$

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#abstract-algebra #ring-theory
397
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Maximal ideals of $C(X, \mathbb R)$

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#abstract-algebra #ring-theory #maximal-and-prime-ideals
61
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Struggling to understand principal ideals in Ring Theory

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#ring-theory #ideals
421
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How to show $\langle 7\rangle$ is a prime ideal of $\Bbb Z[x]$

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#ring-theory #ideals
33
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Operation on ideals of Frobenius algebra

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#abstract-algebra #ring-theory #algebras
57
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Factorisation of an Ideal via Ideals Generated using its Norm

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#ring-theory #algebraic-number-theory #normed-spaces #ideals #coprime
29
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If field $K$ splits $S$, a central simple algebra over field $k \subset K$, then $K' \supset K$ splits $S$.

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#abstract-algebra #ring-theory #noncommutative-algebra

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