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Definition of irreducible element.

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#abstract-algebra #ring-theory #integral-domain
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Building quotient rings

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#abstract-algebra #ring-theory #noncommutative-algebra #finite-rings
2.9k
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Examples of non commutative rings.

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#abstract-algebra #ring-theory
85
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In a ring R, if there exists a in R s.t. ab=0 for any b in R, then a must be 0. Is this statement true?

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#abstract-algebra #ring-theory
650
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Is $\mathbb{Z}[\sqrt{2} + \sqrt{3}]$ closed under multiplication?

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#abstract-algebra #ring-theory #algebraic-number-theory
213
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Finding a Prime Ideal in the Ring of $C^\infty$ Functions

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#real-analysis #ring-theory
43
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Definition of a ring S being finitely generated as an R-algebra

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#ring-theory #definition
195
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Intersection of ideals $I=(2x)$ and $J=(2x^2)$ of $\mathbb{Z}[2x,2x^2,2x^3,\dots]$ is not finitely generated.

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#abstract-algebra #ring-theory #self-learning #principal-ideal-domains #unique-factorization-domains
345
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On factorization of polynomials

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#abstract-algebra #polynomials #ring-theory #irreducible-polynomials
2k
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Defining algebras over noncommutative rings

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#ring-theory #soft-question #category-theory #modules #noncommutative-algebra
152
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Maximal ideal which isn't principal

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#abstract-algebra #ring-theory #ideals
624
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Depth zero module and $R$-regular element

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#ring-theory #commutative-algebra #noetherian
183
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Proving that a field of characteristic $0$ is the field of fractions of a proper subring.

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#ring-theory #field-theory
120
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Prove that $g:R/\ker(φ)\to \operatorname{Ιm}(\varphi)$ where $ g(\ker \varphi+r)=\varphi(r)$ is $1$-$1$

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#abstract-algebra #ring-theory
806
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Maximal linearly independent sets in a f.g. module

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

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