Question

How is this proof correct in regard to a $k$-subalgebra (Eisenbud)?

score 136 · Answer 1 · 2026-03-26 05:16:56

136

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How is this proof correct in regard to a $k$-subalgebra (Eisenbud)?

Published on 26 Mar 2026 - 5:16

score 76 · Answer 2 · 2026-03-26 05:16:56

76

Views

If $f \in \hat{m} = $ largest homogeneous ideal, then each coefficient in some generation is homogeneous.

Published on 26 Mar 2026 - 5:16

score 597 · Answer 3 · 2026-04-07 19:14:13

597

Views

Jacobson Radical of External Direct Sum of Rings

Published on 07 Apr 2026 - 19:14

score 303 · Answer 4 · 2017-03-16 18:15:28

303

Views

Eisenbud: if $A$ is a finitely generated $k$-algebra, then after choosing generators, $A = k[x_1, \dots, x_n]/I$ for some ideal $I$.

Published on 16 Mar 2017 - 18:15

score 785 · Answer 5 · 2026-03-27 07:50:44

785

Views

how to formally prove that $R[x]/ \langle f(x)\rangle$ is isomorphic to $R[α]$

Published on 27 Mar 2026 - 7:50

score 312 · Answer 6 · 2017-03-17 06:23:02

312

Views

Does there exist a proper, non-principal ideal whose radical is principal.

Published on 17 Mar 2017 - 6:23

score 12k · Answer 7 · 2017-03-17 23:24:27

12k

Views

Is a product of ideals the same as intersection of ideals?

Published on 17 Mar 2017 - 23:24

score 431 · Answer 8 · 2026-03-25 06:06:21

431

Views

Product of Principal Ideals when $R$ is commutative, but not necessarily unital

Published on 25 Mar 2026 - 6:06

score 92 · Answer 9 · 2017-03-19 01:35:12

92

Views

Help showing that set of all finite sums of $rx + lx$ is an ideal of commutative ring $R$.

Published on 19 Mar 2017 - 1:35

score 48 · Answer 10 · 2017-03-19 03:08:15

48

Views

Equivalence of two definitions of primary ideals

Published on 19 Mar 2017 - 3:08

score 533 · Answer 11 · 2026-03-25 21:51:15

533

Views

Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?

Published on 25 Mar 2026 - 21:51

score 504 · Answer 12 · 2026-03-26 07:34:53

504

Views

Homomorphic images of $\mathbb{Z}_{n}$

Published on 26 Mar 2026 - 7:34

score 977 · Answer 13 · 2026-04-01 03:45:40

977

Views

Show that the set of prime ideals of A has minimal element with respect to inclusion

Published on 01 Apr 2026 - 3:45

score 368 · Answer 14 · 2026-04-01 03:42:57

368

Views

For a ring $R$ with a single proper ideal $I$, show that $I$ is prime

Published on 01 Apr 2026 - 3:42

score 101 · Answer 15 · 2026-03-25 15:42:22

101

Views

Under what circumstances does the set $\bar G$ obtained by removing some elements of a Gröbner basis remain a Gröbner basis for $\langle\bar G\rangle$

Published on 25 Mar 2026 - 15:42

List Question

How is this proof correct in regard to a $k$-subalgebra (Eisenbud)?

If $f \in \hat{m} = $ largest homogeneous ideal, then each coefficient in some generation is homogeneous.

Jacobson Radical of External Direct Sum of Rings

Eisenbud: if $A$ is a finitely generated $k$-algebra, then after choosing generators, $A = k[x_1, \dots, x_n]/I$ for some ideal $I$.

how to formally prove that $R[x]/ \langle f(x)\rangle$ is isomorphic to $R[α]$

Does there exist a proper, non-principal ideal whose radical is principal.

Is a product of ideals the same as intersection of ideals?

Product of Principal Ideals when $R$ is commutative, but not necessarily unital

Help showing that set of all finite sums of $rx + lx$ is an ideal of commutative ring $R$.

Equivalence of two definitions of primary ideals

Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?

Homomorphic images of $\mathbb{Z}_{n}$

Show that the set of prime ideals of A has minimal element with respect to inclusion

For a ring $R$ with a single proper ideal $I$, show that $I$ is prime

Under what circumstances does the set $\bar G$ obtained by removing some elements of a Gröbner basis remain a Gröbner basis for $\langle\bar G\rangle$

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