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Nilpotent Elements and Intersection of Prime Ideals

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#ring-theory #ideals #radicals
149
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Size of an ideal in a polynomial Ring

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#polynomials #ring-theory #ideals
817
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Why is the completion of the ring of germs of smooth functions isomorphic to $\mathbb{R}[[T]]$?

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#real-analysis #ring-theory #commutative-algebra
82
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Suppose $R$ is a ring and $\exists n \in \mathbb{Z}_{> 0}$ such that $(ab)^n=ab, \forall a,b \in R.$ Then $ab = 0 $ iff $ba=0 \ ?$

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#ring-theory
162
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Generality of rings' abelian group

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#group-theory #ring-theory #finite-groups
315
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Rings act on modules

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#abstract-algebra #ring-theory #modules
989
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Definition of modules

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#abstract-algebra #ring-theory #modules
1k
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Finding the conjugates in $\mathbb{C}$ of a given number over a given field...

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#polynomials #ring-theory #field-theory #irreducible-polynomials
131
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An attempt to verify if $\mathbb{Z}_{7^5}$ a local ring with unique maximal ideal $(7) \ .$

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#ring-theory
569
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Why study integrality?

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#ring-theory #commutative-algebra #algebraic-number-theory #intuition #motivation
58
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Is $2\mathbb{Z}_{12}$ maximal ideal of $\mathbb{Z}_{12} \ ?$

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#ring-theory
298
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Fraction field of $R/P$

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#abstract-algebra #ring-theory #commutative-algebra
70
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If $R$ is $\text{PID}$ and $x \in R$ is irreducible, then $R/(x^k)$ is a local ring.

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#ring-theory
5.4k
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Spectrum of a product of rings isomorphic to the product of the spectra

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#abstract-algebra #ring-theory #commutative-algebra #ideals
192
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Example of Localization and Prime Ideals

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#ring-theory #commutative-algebra #examples-counterexamples #ideals

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