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15
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Show that $K $ is prime ideal of $K $

Published on
#ring-theory #field-theory #ideals #maximal-and-prime-ideals
145
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Question About Definition of Subring

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#abstract-algebra #ring-theory
190
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Socle of sum is the sum of socles

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#ring-theory #modules #representation-theory #noncommutative-algebra
25
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Noetherian ring is finitely generated

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#abstract-algebra #ring-theory #ideals #axiom-of-choice #noetherian
64
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Find $f \in \mathbb{Q}(X)$ so that the ideal $(2,X)f = (2f,Xf) \subset \mathbb{Z}[X]$

Published on
#ring-theory #gcd-and-lcm
83
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Ring of invariants of $R \otimes_k \bar{k}$ under Galois action

Published on
#abstract-algebra #ring-theory #commutative-algebra #galois-theory
74
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Do these module theorems in algebra have a right version?

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#abstract-algebra #ring-theory #modules #semi-simple-rings
881
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Irreducible element of $\mathbb{Z}[\sqrt{-d}]$ generating an ideal that isn't prime

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
234
Views

Show that $(M_n(R))[X]\cong M_n(R[X])$

Published on
#matrices #ring-theory #polynomial-rings
58
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If $R/k$ is a ring extension, with $k$ a field, $R$ a integer domain, $[R:k]=n\in\mathbb{N}\implies R$ is a field

Published on
#ring-theory #field-theory #extension-field
82
Views

Is there a name for the number system that's like $\mathbb{Q}$ but without the cancellation law $ax/bx = a/b$?

Published on
#abstract-algebra #number-theory #ring-theory #dirichlet-series
45
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Prove $I=\{r\in R\vert rL\subseteq N\}$ is an ideal of $R$.

Published on
#ring-theory #modules #ideals
437
Views

Proof that the polynomial ring over a field is catenary.

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#abstract-algebra #polynomials #ring-theory #commutative-algebra
17
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Infinitely many non-equivalent decompositions into irreducibles

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#abstract-algebra #ring-theory
262
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Invariant polynomials on $\mathfrak{gl} (r,F)$ given the map $\varepsilon$ from polynomials to polynomial functions might not be injective

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#abstract-algebra #differential-geometry #polynomials #ring-theory #vector-spaces

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