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15
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A local subring of $F[[x]]$?

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#ring-theory #commutative-algebra #ideals
447
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Is there a (hypercomplex) number system, in which addition is **not** commutative

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#abstract-algebra #ring-theory #noncommutative-algebra #quaternions
176
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Are there categorifications of prime or irreducible elements (of a ring, say)?

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#ring-theory #category-theory #soft-question #categorification
104
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To show a certain integral closure is an order.

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#abstract-algebra #ring-theory #commutative-algebra #dedekind-domain
325
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$A$ a ring, ($\exists n\in\mathbb{N},n\geq 2,\ \forall x\in A$, $x^n=x$) $\Rightarrow$ A is commutative?

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#abstract-algebra #ring-theory
2.4k
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Find all ideals of $\mathbb R[x] / \langle x^2-3x+2\rangle$

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#abstract-algebra #ring-theory #ideals
160
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How to define average operator on the Real (semi) ring

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#abstract-algebra #ring-theory
65
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Finding all homomorphisms and proving a solution exists

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#abstract-algebra #ring-theory
271
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Commutative ring with an ideal that contains all the nonunits

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#abstract-algebra #ring-theory #commutative-algebra #ideals
65
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Showing that $\frac{\mathbb{C}[X]}{<x-1>}$ is isomorphic to $\mathbb{C}$

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#ring-theory #field-theory
372
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Minimal set of generators VS Length of a module.

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#ring-theory #modules
79
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Let $R$ be a UFD and $p,q,r \in R$. $pq=r^3$ and $\gcd(p,q)=1$ then $p,q$ are cubes up to associates.

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#abstract-algebra #ring-theory #unique-factorization-domains
2.5k
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Must an ideal generated by an irreducible element be a maximal ideal?

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#abstract-algebra #ring-theory
364
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Ring extension and Jacobson rings

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#algebraic-geometry #ring-theory #commutative-algebra
13k
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Multiplicative inverse of $0$

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#abstract-algebra #ring-theory #inverse

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