List questions from integral-domain

Published on 05 Feb 2015 - 12:33

458

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Prove that $M/\mathrm{Tor}(M)$ is an R-module with zero torsion

Published on 07 Feb 2015 - 2:54

1.1k

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Show that $A[X]/(aX+b)$ is an integral domain

Published on 08 Feb 2015 - 20:24

42

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Homomorphism from $A[X,Y]$ to $A[X]$ with kernel $(X^i-Y^j)$

Published on 08 Feb 2015 - 21:20

116

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Prove that if $a$ divides both $2$ and $\sqrt{10}$ in $\mathbb{Z}[\sqrt{10}]$, then $a$ is a unit

Published on 17 Feb 2015 - 1:10

742

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In $R[x]$, $f=g \iff f(x)=g(x), \forall x \in R$

Published on 24 Feb 2015 - 1:20

591

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Existence of Zero Divisors in $C(X,\mathbb{R})$

Published on 05 Mar 2015 - 6:22

52

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Manipulations of Euclidean domains

Published on 08 Mar 2015 - 15:52

327

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Intersection of ring and prime ideal

Published on 10 Mar 2015 - 3:44

580

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Quotient ring of complex polynomials and ideal domain

Published on 16 Mar 2015 - 0:54

607

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Extension of Integral Domains

Published on 25 Mar 2026 - 4:39

748

Views

Does validity of Bezout identity in integral domain implies the domain is PID?

Published on 26 Mar 2015 - 13:49

302

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Let $R$ be a commutative ring with no zero divisors, then $R$ can be embedded in an integral domain $S$.

Published on 30 Mar 2015 - 16:11

514

Views

A noetherian local ring having a height one principal prime is a domain

Published on 03 Apr 2015 - 17:21

58

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Is it true that for any integral domain $D$ , $\text{Frac}(D)[x] \cong \text{Frac}(D[x])$?

Published on 06 Apr 2015 - 15:30

List Question

Algebraic characterization of commutative rings with Krull dimension=1,2, or 3

Prove that $M/\mathrm{Tor}(M)$ is an R-module with zero torsion

Show that $A[X]/(aX+b)$ is an integral domain

Homomorphism from $A[X,Y]$ to $A[X]$ with kernel $(X^i-Y^j)$

Prove that if $a$ divides both $2$ and $\sqrt{10}$ in $\mathbb{Z}[\sqrt{10}]$, then $a$ is a unit

In $R[x]$, $f=g \iff f(x)=g(x), \forall x \in R$

Existence of Zero Divisors in $C(X,\mathbb{R})$

Manipulations of Euclidean domains

Intersection of ring and prime ideal

Quotient ring of complex polynomials and ideal domain

Extension of Integral Domains

Does validity of Bezout identity in integral domain implies the domain is PID?

Let $R$ be a commutative ring with no zero divisors, then $R$ can be embedded in an integral domain $S$.

A noetherian local ring having a height one principal prime is a domain

Is it true that for any integral domain $D$ , $\text{Frac}(D)[x] \cong \text{Frac}(D[x])$?

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