Question

Proof of: if A is an integral domain, then the units of A[x] are the constant polynomials that are units of A

score 1.4k · Answer 1 · 2019-11-21 19:21:48

1.4k

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Proof of: if A is an integral domain, then the units of A[x] are the constant polynomials that are units of A

Published on 21 Nov 2019 - 19:21

score 556 · Answer 2 · 2019-11-22 06:54:45

556

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GCD in Integral Domains

Published on 22 Nov 2019 - 6:54

score 122 · Answer 3 · 2019-11-22 16:51:24

122

Views

Quotient rings link to first isomorphism theorem

Published on 22 Nov 2019 - 16:51

score 318 · Answer 4 · 2026-03-25 15:51:32

318

Views

Monic associates of Polynomials over Integral Domains

Published on 25 Mar 2026 - 15:51

score 173 · Answer 5 · 2019-11-24 04:00:46

173

Views

Prove that if $a$ is a root of $fg$, $a$ is a root of $f$ or $a$ is a root of $g$.

Published on 24 Nov 2019 - 4:00

score 89 · Answer 6 · 2026-03-25 20:15:19

89

Views

A variation on $6=2 \cdot 3=(1+\sqrt {-5})(1-\sqrt {-5})$

Published on 25 Mar 2026 - 20:15

score 514 · Answer 7 · 2019-12-04 23:29:14

514

Views

Let $R$ be an integral domain and $p,q \in R$. Is it true that $(pq)R = pR \cap qR$?

Published on 04 Dec 2019 - 23:29

score 268 · Answer 8 · 2019-12-06 03:42:22

268

Views

Is there a relationship between a polynomial and the $\gcd$ of its coefficients?

Published on 06 Dec 2019 - 3:42

score 115 · Answer 9 · 2019-12-07 20:04:36

115

Views

If $A$ is a DVR such that $k\subset A\subset k(x)$, $Frac(A)=k(x)$ and $x\not\in A$, then $A=\mathcal{O}_{\infty}(k)$

Published on 07 Dec 2019 - 20:04

score 34 · Answer 10 · 2026-03-25 12:50:07

34

Views

Showing the existence of a certain kind of extension of a finitely generated algebra

Published on 25 Mar 2026 - 12:50

score 100 · Answer 11 · 2019-12-27 03:56:07

100

Views

Example of $S$-Noetherian rings

Published on 27 Dec 2019 - 3:56

score 891 · Answer 12 · 2020-01-04 16:16:16

891

Views

Find the kernel of a homomorphism between polynomial rings

Published on 04 Jan 2020 - 16:16

score 498 · Answer 13 · 2020-01-11 12:14:34

498

Views

Does the cancellation property for a group mean something different than the cancellation property for an integral domain?

Published on 11 Jan 2020 - 12:14

score 82 · Answer 14 · 2020-01-16 19:13:34

82

Views

Integral domain and localization

Published on 16 Jan 2020 - 19:13

score 40 · Answer 15 · 2020-01-23 17:47:13

40

Views

Rings with rectangles with same perimeter but different surface

Published on 23 Jan 2020 - 17:47

List Question

Proof of: if A is an integral domain, then the units of A[x] are the constant polynomials that are units of A

GCD in Integral Domains

Quotient rings link to first isomorphism theorem

Monic associates of Polynomials over Integral Domains

Prove that if $a$ is a root of $fg$, $a$ is a root of $f$ or $a$ is a root of $g$.

A variation on $6=2 \cdot 3=(1+\sqrt {-5})(1-\sqrt {-5})$

Let $R$ be an integral domain and $p,q \in R$. Is it true that $(pq)R = pR \cap qR$?

Is there a relationship between a polynomial and the $\gcd$ of its coefficients?

If $A$ is a DVR such that $k\subset A\subset k(x)$, $Frac(A)=k(x)$ and $x\not\in A$, then $A=\mathcal{O}_{\infty}(k)$

Showing the existence of a certain kind of extension of a finitely generated algebra

Example of $S$-Noetherian rings

Find the kernel of a homomorphism between polynomial rings

Does the cancellation property for a group mean something different than the cancellation property for an integral domain?

Integral domain and localization

Rings with rectangles with same perimeter but different surface

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