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15
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Is the ring $\mathbb{Z}_{p^n}$ local?

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#abstract-algebra #ring-theory #local-rings
111
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Let $p>2$ ,Existence of $a,b \in \mathbb{Z}$ such that $a^2+2b^2=p$.

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#abstract-algebra #ring-theory
67
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Is $\mathbb{Z}[X]/(I+J)$ integral domain

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#abstract-algebra #ring-theory #integral-domain
1.1k
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How can i find a inverse of a polynomial in a quotient ring?

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#abstract-algebra #polynomials #ring-theory #inverse
24
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Operation that selects a unique representative from each class of associate elements

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#ring-theory #soft-question #terminology #divisibility
2.4k
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Why isn't $\frac{1}{x}$ a polynomial?

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#abstract-algebra #polynomials #ring-theory
233
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dual isomorphism

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#abstract-algebra #ring-theory #abelian-groups
266
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The fields involved in algebraic geometry / polynomial rings

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#algebraic-geometry #ring-theory
55
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Endomorphism Ring: $f$ zero divisor $\iff$ $\dim Im f< \dim V$

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#linear-algebra #ring-theory #vector-spaces #linear-transformations
85
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Show that the polynomials in $\mathbb C[x,y]$ that contain no terms of the form $cy^m$ form a non-Noetherian subring

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#abstract-algebra #ring-theory
60
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Irreducible elements in a factor ring

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#abstract-algebra #polynomials #ring-theory #factoring #irreducible-polynomials
168
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Ring Homomorphism Counterexample

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#abstract-algebra #ring-theory #ring-homomorphism
340
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The ideal generated by an irreducible element contains a prime ideal implies that the element is prime in a non-UFD?

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#abstract-algebra #ring-theory #integral-domain
18
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Show that $G: Z[t] → \mathbb{C}$ defined by $G(f)=f(\sqrt{-1})$ is a ring homomorphism with kernel $(t^2 + 1)$ and image the Gaussian integers.

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#ring-theory
125
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On a subring of the Laurent polynomials ring

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

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