Question

Prove that $R/I$ and $S/\phi(I)$ are isomorphic

score 1.1k · Answer 1 · 2019-11-11 07:06:27

1.1k

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Prove that $R/I$ and $S/\phi(I)$ are isomorphic

Published on 11 Nov 2019 - 7:06

score 140 · Answer 2 · 2019-11-12 03:23:57

140

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If I is an ideal of R (considering I as an additive subgroup of R), elements of the factor ring/group (R/I).

Published on 12 Nov 2019 - 3:23

score 108 · Answer 3 · 2019-11-12 14:45:33

108

Views

Showing an ideal is principal.

Published on 12 Nov 2019 - 14:45

score 95 · Answer 4 · 2026-03-26 06:21:34

95

Views

If $x \in \cap_{n=1}^\infty I^n$, then $x \in xI$.

Published on 26 Mar 2026 - 6:21

score 30 · Answer 5 · 2026-03-27 23:35:25

30

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Correspondence between $l$-quasi-cyclic codes over $GF(q)$ of length $ml$ and left ideal of $ M_{l}(GF(q))[X]/(X^{m}-1) $

Published on 27 Mar 2026 - 23:35

score 99 · Answer 6 · 2026-03-31 00:08:03

99

Views

Using the Minkowski bound to prove that a ring is principal

Published on 31 Mar 2026 - 0:08

score 78 · Answer 7 · 2019-11-16 01:30:36

78

Views

About minimal ideals and division rings

Published on 16 Nov 2019 - 1:30

score 59 · Answer 8 · 2019-11-16 16:16:28

59

Views

Struggling to understand principal ideals in Ring Theory

Published on 16 Nov 2019 - 16:16

score 418 · Answer 9 · 2019-11-16 18:45:19

418

Views

How to show $\langle 7\rangle$ is a prime ideal of $\Bbb Z[x]$

Published on 16 Nov 2019 - 18:45

score 56 · Answer 10 · 2026-02-23 08:38:31

56

Views

Factorisation of an Ideal via Ideals Generated using its Norm

Published on 23 Feb 2026 - 8:38

score 71 · Answer 11 · 2019-11-17 03:31:53

71

Views

How to find polynomial multipliers that relate a specific element in the Groebner basis to the original generators?

Published on 17 Nov 2019 - 3:31

score 178 · Answer 12 · 2019-11-18 22:57:30

178

Views

Commutative algebra: operations on ideals

Published on 18 Nov 2019 - 22:57

score 302 · Answer 13 · 2026-03-30 05:16:50

302

Views

Correspondence Theorem for maximal ideals.

Published on 30 Mar 2026 - 5:16

score 62 · Answer 14 · 2026-04-02 05:21:35

62

Views

About Primary Decomposition - $\displaystyle\cup^n_{i=1}\mathfrak{p}_i=\{x\in A:(\mathfrak{a}:x)\neq\mathfrak{a}\}$

Published on 02 Apr 2026 - 5:21

score 243 · Answer 15 · 2019-11-19 15:17:18

243

Views

Maximal ideal among those that are not finitely generated

Published on 19 Nov 2019 - 15:17

List Question

Prove that $R/I$ and $S/\phi(I)$ are isomorphic

If I is an ideal of R (considering I as an additive subgroup of R), elements of the factor ring/group (R/I).

Showing an ideal is principal.

If $x \in \cap_{n=1}^\infty I^n$, then $x \in xI$.

Correspondence between $l$-quasi-cyclic codes over $GF(q)$ of length $ml$ and left ideal of $ M_{l}(GF(q))[X]/(X^{m}-1) $

Using the Minkowski bound to prove that a ring is principal

About minimal ideals and division rings

Struggling to understand principal ideals in Ring Theory

How to show $\langle 7\rangle$ is a prime ideal of $\Bbb Z[x]$

Factorisation of an Ideal via Ideals Generated using its Norm

How to find polynomial multipliers that relate a specific element in the Groebner basis to the original generators?

Commutative algebra: operations on ideals

Correspondence Theorem for maximal ideals.

About Primary Decomposition - $\displaystyle\cup^n_{i=1}\mathfrak{p}_i=\{x\in A:(\mathfrak{a}:x)\neq\mathfrak{a}\}$

Maximal ideal among those that are not finitely generated

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