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Finite rings and subrings isomorphic to $\mathbb{Z}_n$

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#abstract-algebra #ring-theory
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How to prove $e^{A \oplus B} = e^A \otimes e^B$ where $A$ and $B$ are matrices? (Kronecker operations)

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#linear-algebra #abstract-algebra #group-theory #ring-theory #quantum-mechanics
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Is quotient module finitely generated?

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#abstract-algebra #ring-theory #modules
478
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Localization of an integer quotient is a field

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#abstract-algebra #commutative-algebra #ring-theory
67
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Ring Embeds in Monoid Ring

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#ring-theory #proof-writing #monoid
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Proving that the units of a ring form a group under multiplication

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#abstract-algebra #group-theory #ring-theory #solution-verification
710
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A non-zero and non-invertible element in a noetherian integral domain has a decomposition into irreducible elements

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#abstract-algebra #ring-theory #ideals #noetherian
63
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Degree 3 polynomial with coef in a field K: question on roots in a algebraic closure

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#abstract-algebra #polynomials #ring-theory #galois-theory #field-theory
3.8k
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Polynomial rings over a field and maximal/prime ideals

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#abstract-algebra #ring-theory #ideals
67
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Intersection of Ideals in a ring

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#abstract-algebra #ring-theory
98
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$f(x) \mid g(x) \iff g(x) \in \langle f(x) \rangle$. Isn't this trivial?

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#ring-theory #field-theory
1.4k
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Regarding Irreducibility of two variable polynomial

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#abstract-algebra #ring-theory #irreducible-polynomials
226
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How can I complete the proof of Noetherianity of I. S. Cohen?

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#abstract-algebra #commutative-algebra #ring-theory #finitely-generated
374
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A Lemma of Kaplansky

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#abstract-algebra #ring-theory #proof-explanation
720
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Polynomials over a field with characteristic $0$ is square free implies it's coprime with its formal derivative

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#abstract-algebra #polynomials #ring-theory

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