Question

Show that there is no finite ordered integral domain.

score 349 · Answer 1 · 2020-10-21 05:37:51

349

Views

Show that there is no finite ordered integral domain.

Published on 21 Oct 2020 - 5:37

score 255 · Answer 2 · 2026-03-26 16:05:09

255

Views

Show that $K [\Bbb Z]$ is an integral domain.

Published on 26 Mar 2026 - 16:05

score 289 · Answer 3 · 2020-10-29 07:06:48

289

Views

Prove or disprove that $A[x]/I$ is an integral domain.

Published on 29 Oct 2020 - 7:06

score 40 · Answer 4 · 2020-11-02 19:37:21

40

Views

There is a unique binary relation $<$ which turn the integral domain $(\mathbb{Z},+,\times)$ into an ordered integral domain.

Published on 02 Nov 2020 - 19:37

score 64 · Answer 5 · 2026-03-27 19:10:12

64

Views

Comparing proof of $R[[x]]^$ consists of $\sum_{n \geq 0}a_{n}x^n (a_{n} \in R) ,a_{0} \in R^ ,R$ an integral domain to $R$ a ring.

Published on 27 Mar 2026 - 19:10

score 162 · Answer 6 · 2020-11-10 03:30:32

162

Views

Reference on different types of integral domains

Published on 10 Nov 2020 - 3:30

score 249 · Answer 7 · 2026-03-28 23:59:09

249

Views

Show that $Z^2 + Y^3 + X^5$ is irreducible in $\mathbb C[X,Y,Z].$

Published on 28 Mar 2026 - 23:59

score 975 · Answer 8 · 2020-11-20 06:55:41

975

Views

Show that if $\mathfrak{p} \subset R$ is a prime ideal, then $S = R \setminus \mathfrak{p}$ is multiplicatively closed.

Published on 20 Nov 2020 - 6:55

score 1k · Answer 9 · 2026-03-28 09:53:32

1k

Views

Can a direct product $R\times X$ of two integral domains $R$ and $X$ ever be an integral domain?

Published on 28 Mar 2026 - 9:53

score 67 · Answer 10 · 2020-11-29 12:54:31

67

Views

Gauss lemma for Irreducibility over $\mathbb{Z}\bigl[\sqrt{13}\mkern2mu\bigr]$

Published on 29 Nov 2020 - 12:54

score 217 · Answer 11 · 2020-12-01 00:21:08

217

Views

Localisation of an integral domain

Published on 01 Dec 2020 - 0:21

score 831 · Answer 12 · 2020-12-01 19:32:25

831

Views

How to Prove or disprove : Let I be an ideal of R and R/I be a integral domain then R is an integral domain?

Published on 01 Dec 2020 - 19:32

score 57 · Answer 13 · 2026-03-25 22:09:25

57

Views

Tough integration problem - complete the square, domain, absolute value, plus/minus.

Published on 25 Mar 2026 - 22:09

score 62 · Answer 14 · 2020-12-03 01:58:45

62

Views

Prove that $\mathbb{Z}[\omega]$ with $\omega^p=1$ is an integral domain.

Published on 03 Dec 2020 - 1:58

score 138 · Answer 15 · 2020-12-05 17:02:06

138

Views

Suppose $A[x]$ is integrally closed then $A$ need not be UFD.

Published on 05 Dec 2020 - 17:02

List Question

Show that there is no finite ordered integral domain.

Show that $K [\Bbb Z]$ is an integral domain.

Prove or disprove that $A[x]/I$ is an integral domain.

There is a unique binary relation $<$ which turn the integral domain $(\mathbb{Z},+,\times)$ into an ordered integral domain.

Comparing proof of $R[[x]]^$ consists of $\sum_{n \geq 0}a_{n}x^n (a_{n} \in R) ,a_{0} \in R^ ,R$ an integral domain to $R$ a ring.

Reference on different types of integral domains

Show that $Z^2 + Y^3 + X^5$ is irreducible in $\mathbb C[X,Y,Z].$

Show that if $\mathfrak{p} \subset R$ is a prime ideal, then $S = R \setminus \mathfrak{p}$ is multiplicatively closed.

Can a direct product $R\times X$ of two integral domains $R$ and $X$ ever be an integral domain?

Gauss lemma for Irreducibility over $\mathbb{Z}\bigl[\sqrt{13}\mkern2mu\bigr]$

Localisation of an integral domain

How to Prove or disprove : Let I be an ideal of R and R/I be a integral domain then R is an integral domain?

Tough integration problem - complete the square, domain, absolute value, plus/minus.

Prove that $\mathbb{Z}[\omega]$ with $\omega^p=1$ is an integral domain.

Suppose $A[x]$ is integrally closed then $A$ need not be UFD.

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