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15
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The reduced basis for a binomial ideal is formed by binomials

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#abstract-algebra #commutative-algebra #groebner-basis #binomial-ideals
56
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Adding a prime number to a special homogeneous prime ideal preserves primeness

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#polynomials #commutative-algebra #irreducible-polynomials #maximal-and-prime-ideals
1k
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Localization of maximal ideal is again a maximal ideal and the residue fields are isomorphic

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#abstract-algebra #ring-theory #commutative-algebra #localization
54
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Is $\bigcap_{i\in I}(M_i/N)=\bigl(\bigcap_{i\in I}M_i\bigr)/N$?

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#abstract-algebra #commutative-algebra #modules #quotient-spaces
140
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localizations and overrings of Dedekind domains with prescribed spectrum

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#ring-theory #commutative-algebra #algebraic-number-theory #localization #dedekind-domain
100
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The Tropical Semiring is Local?

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#abstract-algebra #commutative-algebra #semiring
988
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Finite dimensional associative division algebras over Q

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#abstract-algebra #ring-theory #vector-spaces #commutative-algebra #field-theory
81
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References for sufficiency of tangential criteria for formally smooth/unramified/étale morphisms

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#algebraic-geometry #commutative-algebra #schemes #affine-schemes
61
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A function on ideals that converts intersection to sum

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#algebraic-geometry #commutative-algebra #ideals
377
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Describe the corresponding $k$-algebra homomorphism $\tilde{\varphi}:k[V]\to k[\mathbb{A}^1]$.

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#abstract-algebra #commutative-algebra #affine-varieties #morphism
108
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Taking quotients is left exact

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#ring-theory #commutative-algebra
90
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Conditions that a module has a unique largest divisible submodule.

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#abstract-algebra #commutative-algebra #modules #dedekind-domain
96
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Distributive law over submodules

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#abstract-algebra #ring-theory #commutative-algebra
33
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Why is it that $S \subset (sa^n: s \in S, n > 0)$ for any $a \in A$?

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#ring-theory #commutative-algebra
1k
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product of two algebras is still a algebra?

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#commutative-algebra #tensor-products

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