List questions from integral-domain

Published on 25 Dec 2020 - 18:20

419

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Morphism between integral domain and field is injective?

Published on 27 Mar 2026 - 12:26

93

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When is an integral domain a localization of a proper subring?

Published on 02 Jan 2021 - 18:52

57

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Decompose an ideal into sum of a product with maximal ideal and a principal ideal.

Published on 04 Jan 2021 - 12:40

92

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Non-constant polynomial over an integral domain without any irreducible factors.

Published on 14 Jan 2021 - 1:50

126

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$\mathbb{Z}_p$ with $p$ prime is integral domain

Published on 18 Jan 2021 - 10:19

64

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Let R be a commutative non-trivial ring. Show that R is torsion-free iff R is an integral domain. Proof check.

Published on 19 Jan 2021 - 2:50

116

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What kind of subrings inherit their parent ring's properties?

Published on 20 Jan 2021 - 14:32

298

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Field of fractions of $R = \{ \frac{a}{b} | \ a \in \mathbb{Z}, b \in \mathbb{Z} \setminus p\mathbb{Z} \}$.

Published on 23 Jan 2021 - 12:16

142

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Is it possible to factor a polynomial over a ring which is not an integral domain?

Published on 26 Jan 2021 - 21:47

105

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Integral closure in an extension ring

Published on 14 Feb 2021 - 3:41

640

Views

Prove that $ k[x,y]/(x^3 - y^2)$ is not a UFD.

Published on 17 Feb 2021 - 8:49

42

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Isomorphism between polynomial rings and its restriction

Published on 19 Feb 2021 - 9:22

522

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Find the domain and the area where the vector field is conservative!

Published on 21 Feb 2021 - 18:37

158

Views

irreducible over $\mathbb R[x,y]$

Published on 23 Feb 2021 - 19:05

List Question

For commutative rings, if the ring of polynomials is a PID then the ring is an integral domain.

Morphism between integral domain and field is injective?

When is an integral domain a localization of a proper subring?

Decompose an ideal into sum of a product with maximal ideal and a principal ideal.

Non-constant polynomial over an integral domain without any irreducible factors.

$\mathbb{Z}_p$ with $p$ prime is integral domain

Let R be a commutative non-trivial ring. Show that R is torsion-free iff R is an integral domain. Proof check.

What kind of subrings inherit their parent ring's properties?

Field of fractions of $R = \{ \frac{a}{b} | \ a \in \mathbb{Z}, b \in \mathbb{Z} \setminus p\mathbb{Z} \}$.

Is it possible to factor a polynomial over a ring which is not an integral domain?

Integral closure in an extension ring

Prove that $ k[x,y]/(x^3 - y^2)$ is not a UFD.

Isomorphism between polynomial rings and its restriction

Find the domain and the area where the vector field is conservative!

irreducible over $\mathbb R[x,y]$

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