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Let $\varphi : R \rightarrow S$ be a ring homomorphism and $T \subseteq R$. Prove that $\varphi(r)$ is integral over $\varphi(T)$.

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#abstract-algebra #ring-theory #commutative-algebra
66
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Branch of Math That Links Indicator Function and Expressability in a Ring

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#abstract-algebra #sequences-and-series #ring-theory #special-functions
1.3k
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Krull dimension of a direct product of rings

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#abstract-algebra #ring-theory #commutative-algebra #krull-dimension #direct-product
72
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Why is this element irreducible?

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#abstract-algebra #ring-theory #principal-ideal-domains #unique-factorization-domains
166
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Does every valuation ring arise out of a valuation?

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#abstract-algebra #ring-theory #commutative-algebra #field-theory #valuation-theory
520
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Irreducibility in the polynomial ring over the rationals $\mathbb Q[t]$ versus $\mathbb Z[t]$

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#abstract-algebra #polynomials #ring-theory
245
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$Z[i]/(2+3i) \simeq Z/13Z$ is my proof correct?

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#abstract-algebra #ring-theory #ideals #gaussian-integers
787
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Isomorphic to the quotient ring

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#ring-theory
231
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Calculating the residue field of $\mathbb{F}_q(t)$ with respect to the valuation $-\deg$

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#abstract-algebra #ring-theory #commutative-algebra #valuation-theory
1k
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Ring Homomorphisms, ideals and kernel

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#abstract-algebra #ring-theory
48
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Testing for ideals

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#abstract-algebra #ring-theory
180
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Principal ideal of a unit

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#abstract-algebra #ring-theory #ideals
73
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Coordinate ring of $V \subset \mathbb{A}^n$ variety

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#abstract-algebra #algebraic-geometry #ring-theory #commutative-algebra #algebraic-curves
71
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Integral Elements of $\mathbb{Q[x]}$ in $\mathbb{Q(x)}$

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#abstract-algebra #ring-theory #commutative-algebra
77
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Different discrete valuation rings inside the same fraction field

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#ring-theory #valuation-theory

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