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How to show the following ring is not Noetherian

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#abstract-algebra #ring-theory #noetherian
72
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How is an arbitrary member of $\mathbb{Q}(\pi)$ defined?

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#ring-theory #extension-field
122
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Maximum number of algebraically independent homogeneous polynomials of given degree

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#algebraic-geometry #polynomials #ring-theory #commutative-algebra
361
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If $R$ is a finite ring, then $\exists_{n>m>0}: x^n=x^m$ for all $x\in R$

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#abstract-algebra #ring-theory #finite-rings
85
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Describe explicitly $\text{spec}(\mathbb{R}[x])$ and $\text{spec}(\mathbb{C}[x])$

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#abstract-algebra #ring-theory #zariski-topology #polynomial-rings
89
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An injective homomorphism from $k[x,y]$ to $k[x,x^{-1},y]$

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#ring-theory #commutative-algebra
83
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Computing Intersection of Ideals

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#graph-theory #ring-theory #commutative-algebra #modules
52
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If $A$ and $B$ are rings with unity, prove that $U(A \times B) \cong U(A) \times U(B)$

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#abstract-algebra #ring-theory
139
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Euler theorem's inverse proposition in number theory

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#abstract-algebra #group-theory #number-theory #elementary-number-theory #ring-theory
306
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How to find initial object of the category of pointed rings?

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#ring-theory #category-theory #ring-homomorphism #slice-category
607
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Direct sum of isomorphic simple modules

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#abstract-algebra #ring-theory #modules #representation-theory
55
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What does addition contribute to the concept of unique factorisation in rings?

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#abstract-algebra #group-theory #ring-theory #factoring #unique-factorization-domains
35
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formal definition of operations in the ring of integers $\mathbb{Z}$

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#elementary-number-theory #ring-theory #integers #natural-numbers
150
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Automorphism of a matrices ring

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#linear-algebra #discrete-mathematics #ring-theory #automorphism-group
66
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How to plot ideals of rings

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#ring-theory #ideals #visualization

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