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An example of an ordered UFD except the ring of integers?

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#abstract-algebra #ring-theory #reference-request #ordered-rings
93
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Can you describe all the ways to "un-localize" a ring?

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#abstract-algebra #ring-theory #reference-request #localization
125
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Show that there is no proper ideal of finite presentation of $R$.

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#abstract-algebra #ring-theory #commutative-algebra #modules #finitely-generated
51
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generator of ideal in ring of fraction

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#ring-theory #ideals
32
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Prove that if $f$ is divisible by $h^2$ then h divides gcd(f,f')

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#polynomials #ring-theory #field-theory #gcd-and-lcm
50
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Can $L|K$ be a Galois extension if $\text {Fix}_{G}\ (L) = K$?

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#abstract-algebra #ring-theory #proof-writing #field-theory #galois-theory
267
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Endomorphism ring of module quotient radical

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#abstract-algebra #ring-theory #commutative-algebra #modules #representation-theory
674
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Torsion-free module over a DVR

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#algebraic-geometry #ring-theory #commutative-algebra
93
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What is an elegant way of defining complement of an element in this ring?

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#abstract-algebra #elementary-set-theory #ring-theory #boolean-ring
136
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The elements of $ (\mathbb {Z}/2\mathbb{Z})⊗_{\mathbb {Z}}\mathbb {Z}$

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#abstract-algebra #ring-theory #commutative-algebra #modules #tensor-products
59
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Regular Functions on Disconnected Affine Algebraic Sets

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#algebraic-geometry #ring-theory #affine-geometry
386
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Can a matrix have any characteristic polynomial?

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#linear-algebra #matrices #ring-theory #eigenvalues-eigenvectors #determinant
22
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Is infiniteness of $K$ essential for the isomorphism between coordinate rings and polynomial functions?

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#ring-theory #affine-varieties
84
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Prove or disprove set is an ideal

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#abstract-algebra #ring-theory
112
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Prove $b+x=a$ has one and only one solution

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#abstract-algebra #ring-theory

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