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Any pattern for when the ring $\mathbb{Z}_m$ has units? ($m$ is any integer)

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#abstract-algebra #ring-theory #field-theory #modular-arithmetic #integers
50
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Show that $R = I_1 ⊕ I_2$ is an internal direct sum if and only if there exists $e ^2 = e ∈ C(R)$ such that $I_1 = eR$ and $I_2 = (1 − e)R$.

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#abstract-algebra #ring-theory #ideals #direct-sum
967
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Finite Rings and Product of Finite Fields

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#abstract-algebra #ring-theory #commutative-algebra #finite-fields
678
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Residue field extension

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#abstract-algebra #number-theory #ring-theory #algebraic-number-theory #ideals
619
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Root of unity is a unit in a ring

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#abstract-algebra #ring-theory #roots-of-unity
591
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$k$-algebra morphisms from formal power series ring

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#abstract-algebra #ring-theory #commutative-algebra #formal-power-series
198
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Automorphism trivial on ring of integers quotiented by a prime ideal

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#abstract-algebra #number-theory #ring-theory #field-theory #algebraic-number-theory
91
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Prime ideal and maximal ideal

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#abstract-algebra #ring-theory
37
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Calculating norms of prime ideal by hand

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#abstract-algebra #ring-theory #algebraic-number-theory
462
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What is the point of Hecke $L$-series?

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#abstract-algebra #group-theory #number-theory #ring-theory #algebraic-number-theory
2.9k
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Cohomology Ring Torus

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#ring-theory #algebraic-topology #homology-cohomology #homological-algebra
65
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Hilbert series of agebraically independents polynomial - problem with a proof

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#abstract-algebra #polynomials #ring-theory #solution-verification #hilbert-polynomial
346
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R contains a subring isomorphic to Z/car(R)

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#ring-theory #field-theory
68
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$\mathbb{R}[x,y]/(x^5-y^2)$ is a principal ideal domain?

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#group-theory #elementary-number-theory #ring-theory #irreducible-polynomials
142
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Exercise on Molien theorem

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#abstract-algebra #polynomials #ring-theory #invariant-theory

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