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Ring Theory (idempotents)

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#ring-theory
118
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Rational function in both $k(X)[Y]$ and $k(Y)[X]$

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#polynomials #ring-theory #field-theory #rational-functions
283
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If every element of a ring is either potent or central, the ring is commutative

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#abstract-algebra #ring-theory
145
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$A = B\cdot p(A)$. Show $A$ and $B$ commute.

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#linear-algebra #matrices #ring-theory
242
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kernel of homomorphism $\mathbb{C}[x,y] \to \mathbb{C}[t]$ but in general case

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#abstract-algebra #ring-theory #ideals
831
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A question on ring homomorphisms and maximal ideals.

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#ring-theory
112
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If $x \in R$ is irreducible then $x u$ and $xy$ are irreducible where $u \in R^*$ and $y$ is irreducible.

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#abstract-algebra #ring-theory
529
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Finite Division Rings are Fields

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#abstract-algebra #ring-theory #finite-rings
2.1k
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Preimage of maximal ideal is maximal

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#ring-theory #commutative-algebra #ideals
424
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Self-injective ring but not semisimple?

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#abstract-algebra #ring-theory #modules #injective-module
98
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Find a generator for $(f,g)$, two polynomials in $\mathbb Q[x]$

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#abstract-algebra #ring-theory
216
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Necessary and sufficient condition for a ring homomorphisms property

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#abstract-algebra #ring-theory
13.7k
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How to prove that the evaluation map is a ring homomorphism?

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#abstract-algebra #polynomials #ring-theory
1.1k
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A property of minimal prime ideal

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#abstract-algebra #ring-theory #commutative-algebra
195
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Proving a submodule is Noetherian

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#abstract-algebra #ring-theory #modules #noetherian

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