Question

Is an element of a quotient field of $\mathbb{Z}$ a number or a set?

score 79 · Answer 1 · 2023-04-13 16:07:57

79

Views

Is an element of a quotient field of $\mathbb{Z}$ a number or a set?

Published on 13 Apr 2023 - 16:07

score 125 · Answer 2 · 2023-05-04 09:25:39

125

Views

$A[X, Y ]/(X^2+Y^2−1)$ is integral domain

Published on 04 May 2023 - 9:25

score 36 · Answer 3 · 2023-05-11 13:56:56

36

Views

Under what condition(s) $1) $ is true for a general integral domain $\mathcal{R}$?

Published on 11 May 2023 - 13:56

score 147 · Answer 4 · 2023-05-18 12:30:19

147

Views

Tensor product of a polynomial ring and the quotient of a polynomial ring modulo a prime ideal

Published on 18 May 2023 - 12:30

score 203 · Answer 5 · 2023-05-30 23:14:29

203

Views

Show that $K[x_1,x_2,x_3,x_4] / \langle x_1x_4 - x_2x_3 \rangle$ is an integral domain of dimension $3$

Published on 30 May 2023 - 23:14

score 52 · Answer 6 · 2023-06-01 12:19:35

52

Views

Is $I^n \not = I^{n+1}$ for all non-zero proper ideals $I$ of an integral domain?

Published on 01 Jun 2023 - 12:19

score 39 · Answer 7 · 2023-06-15 11:48:04

39

Views

The difference between two classes of a function

Published on 15 Jun 2023 - 11:48

score 38 · Answer 8 · 2023-06-22 15:37:44

38

Views

"Completion" of an integral domain with irreducible nonprime elements

Published on 22 Jun 2023 - 15:37

score 261 · Answer 9 · 2023-07-09 21:20:22

261

Views

Integral domains with isomorphic field of fractions

Published on 09 Jul 2023 - 21:20

score 42 · Answer 10 · 2023-07-28 04:46:22

42

Views

gcd(a S)= a gcd(S) (integral domain or ufd)

Published on 28 Jul 2023 - 4:46

score 122 · Answer 11 · 2026-03-25 15:57:31

122

Views

When does a semiring extend to an integral domain?

Published on 25 Mar 2026 - 15:57

score 156 · Answer 12 · 2026-03-26 09:26:55

156

Views

Does there exist a surjective but not injective homomorphism of rings from an integral domain R → R

Published on 26 Mar 2026 - 9:26

score 58 · Answer 13 · 2026-03-25 14:30:00

58

Views

Non-toric ring which is Cohen-Macaulay

Published on 25 Mar 2026 - 14:30

score 243 · Answer 14 · 2023-09-28 03:19:39

243

Views

Error in Herstein's "Topics in Algebra", zero ring has characteristic $1$ which is not prime

Published on 28 Sep 2023 - 3:19

score 41 · Answer 15 · 2023-10-04 03:00:51

41

Views

In $f(x)= (x-a_1)(x-a_2)(x-a_3)$, why are the only roots $a_1,a_2,$ and $a_3$ over a prime modulus?

Published on 04 Oct 2023 - 3:00

List Question

Is an element of a quotient field of $\mathbb{Z}$ a number or a set?

$A[X, Y ]/(X^2+Y^2−1)$ is integral domain

Under what condition(s) $1) $ is true for a general integral domain $\mathcal{R}$?

Tensor product of a polynomial ring and the quotient of a polynomial ring modulo a prime ideal

Show that $K[x_1,x_2,x_3,x_4] / \langle x_1x_4 - x_2x_3 \rangle$ is an integral domain of dimension $3$

Is $I^n \not = I^{n+1}$ for all non-zero proper ideals $I$ of an integral domain?

The difference between two classes of a function

"Completion" of an integral domain with irreducible nonprime elements

Integral domains with isomorphic field of fractions

gcd(a S)= a gcd(S) (integral domain or ufd)

When does a semiring extend to an integral domain?

Does there exist a surjective but not injective homomorphism of rings from an integral domain R → R

Non-toric ring which is Cohen-Macaulay

Error in Herstein's "Topics in Algebra", zero ring has characteristic $1$ which is not prime

In $f(x)= (x-a_1)(x-a_2)(x-a_3)$, why are the only roots $a_1,a_2,$ and $a_3$ over a prime modulus?

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