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15
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Sum of nilpotent elements in a noncommutative ring

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#abstract-algebra #ring-theory #nilpotence
55
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Find $u, v$ such that $F\left[x, \frac{1}{x+y}, \frac{1}{y} \right]$ is integral over $F[u, v]$

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#abstract-algebra #ring-theory #commutative-algebra
185
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Explicit description of the map with the nilradical as its kernel

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#ring-theory #nilpotence #ring-homomorphism
64
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The inclusion relation between Ideals

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#ring-theory #ideals
80
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Is a specific endomorphism of $A_1$ an automorphism?

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#ring-theory #noncommutative-algebra
111
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Suppose $R$ is an integral domain and $p$ is a prime ideal

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
64
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Systematic way to show equality between ideals of $K[x,y]$

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#ring-theory #commutative-algebra #ideals #primary-decomposition
60
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Inducing a Peano-style multiplication on a group?

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#abstract-algebra #group-theory #ring-theory #peano-axioms
54
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$K[X]=K(X)$ with X set of algebraic elements

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#abstract-algebra #ring-theory #field-theory
220
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Prime submodules of $\mathbb{Z}×\mathbb{Z}$ as $\mathbb{Z}$-module

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#ring-theory #modules
23
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Proving ring homomorphism between $\ell^\infty$ and $B(H)$

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#abstract-algebra #ring-theory
83
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Prime ideals definition

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#ring-theory
845
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Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain

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#abstract-algebra #ring-theory #commutative-algebra
141
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Subgroup of the direct product of the rings or groups

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#abstract-algebra #group-theory #ring-theory #direct-product
73
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quotient ring which is not local

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#abstract-algebra #ring-theory #commutative-algebra #ideals

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