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Chinese Remainder Theorem: Show that $\phi$ is a Ring homomorphism

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#ring-theory #chinese-remainder-theorem
71
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determine the cardinality and all inverrtible elements of $\mathbb{Z}[x]/(4,x^2)$.

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#abstract-algebra #ring-theory #ideals
54
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Prove: A nonempty subset B of a ring A is closed with respect to addition and negatives iff B is closed with respect to subtraction

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#abstract-algebra #ring-theory
184
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Find prime ideals of Quotient Ring

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#abstract-algebra #ring-theory #field-theory
94
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What does it mean for a map to factorize over something?

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#ring-theory #definition
68
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Computing the kernel of $A[t] \rightarrow K : t \mapsto \frac{a}{b}$.

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#abstract-algebra #ring-theory #commutative-algebra
127
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Identity of the kernel of a ring homomorphism

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#ring-theory
185
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Does the category of $(R,S)$-bimodules contain a free object on one generator?

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#abstract-algebra #ring-theory #category-theory #free-modules #bimodules
85
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Ring theory clarification

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#ring-theory
367
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A Dedekind domain without prime elements

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#ring-theory #commutative-algebra #examples-counterexamples #factoring
48
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Prime property in noncommutative rings without identity

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#abstract-algebra #ring-theory #noncommutative-algebra #rngs
198
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Functor of points of the completion of a ring

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#abstract-algebra #algebraic-geometry #ring-theory #commutative-algebra #formal-completions
2.5k
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Group of units of a field

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#abstract-algebra #group-theory #ring-theory #field-theory #finite-fields
79
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On the natural homomorphism $\nu:R\longrightarrow S^{-1}R$

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#abstract-algebra #ring-theory #localization
573
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Computing $\phi(\frac32)$ where $\phi$ is an automorphism of $\mathbb Q[\sqrt2]$ such that $\phi(1)=1$ and $\phi(\sqrt2)=\sqrt2$

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#abstract-algebra #ring-theory #field-theory #galois-theory

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