Question

Is there a ring containing ideals where the union of the ideals forms a subring but not an ideal?

score 113 · Answer 1 · 2026-03-30 06:29:20

113

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Is there a ring containing ideals where the union of the ideals forms a subring but not an ideal?

Published on 30 Mar 2026 - 6:29

score 75 · Answer 2 · 2019-01-15 04:58:24

75

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Let $f = (x^4 - 1)(x + 2)$ and let $g = (x^2 - 4)(x + 1)$. Find a single polynomial that generates the ideal $I = (f,g)$ of $\mathbb{R}[x]$

Published on 15 Jan 2019 - 4:58

score 1.8k · Answer 3 · 2019-01-15 06:35:50

1.8k

Views

Matrices with all non-zero entries.

Published on 15 Jan 2019 - 6:35

score 57 · Answer 4 · 2026-04-04 03:57:58

57

Views

Determining maximal Cohen-Macaulay modules over an invariant ring

Published on 04 Apr 2026 - 3:57

score 150 · Answer 5 · 2026-03-26 02:55:42

150

Views

Find the smallest positive integer $\ell$ such that $3 \cdot \left(4^m + 1\right)$ divides $2^\ell-1$

Published on 26 Mar 2026 - 2:55

score 1k · Answer 6 · 2026-03-25 06:12:02

1k

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What algebraic structure does the set of endomorphisms of a ring have?

Published on 25 Mar 2026 - 6:12

score 1.1k · Answer 7 · 2026-03-30 06:32:34

1.1k

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Ideals in an infinite direct product of fields

Published on 30 Mar 2026 - 6:32

score 315 · Answer 8 · 2026-03-25 06:09:55

315

Views

Cayley's Theorem for Composition Rings?

Published on 25 Mar 2026 - 6:09

score 173 · Answer 9 · 2026-03-30 15:14:44

173

Views

Are there any references on linear algebra (module theory) over non unital rings?

Published on 30 Mar 2026 - 15:14

score 205 · Answer 10 · 2026-03-28 13:42:02

205

Views

Irrationality of $(a_1+\sqrt{b_1})(a_2+\sqrt{b_2})$

Published on 28 Mar 2026 - 13:42

score 27 · Answer 11 · 2026-03-25 04:43:04

27

Views

Trouble understanding proof regarding elements of an integral domain which are not product of irreducible elements.

Published on 25 Mar 2026 - 4:43

score 514 · Answer 12 · 2019-01-16 02:52:17

514

Views

Veronese embedding as ring isomorphism

Published on 16 Jan 2019 - 2:52

score 225 · Answer 13 · 2026-03-25 02:59:23

225

Views

Can every monoid be turned into a ring?

Published on 25 Mar 2026 - 2:59

score 283 · Answer 14 · 2026-03-26 11:08:42

283

Views

The set of the form $ m+n\sqrt{-3} $, $ m, n\in\mathbb Z $ or $ m, n $ are both halves of odd integers is a Euclidean domain

Published on 26 Mar 2026 - 11:08

score 433 · Answer 15 · 2026-03-28 00:50:56

433

Views

Prove every finite field is of cardinality $p^n$

Published on 28 Mar 2026 - 0:50

List Question

Is there a ring containing ideals where the union of the ideals forms a subring but not an ideal?

Let $f = (x^4 - 1)(x + 2)$ and let $g = (x^2 - 4)(x + 1)$. Find a single polynomial that generates the ideal $I = (f,g)$ of $\mathbb{R}[x]$

Matrices with all non-zero entries.

Determining maximal Cohen-Macaulay modules over an invariant ring

Find the smallest positive integer $\ell$ such that $3 \cdot \left(4^m + 1\right)$ divides $2^\ell-1$

What algebraic structure does the set of endomorphisms of a ring have?

Ideals in an infinite direct product of fields

Cayley's Theorem for Composition Rings?

Are there any references on linear algebra (module theory) over non unital rings?

Irrationality of $(a_1+\sqrt{b_1})(a_2+\sqrt{b_2})$

Trouble understanding proof regarding elements of an integral domain which are not product of irreducible elements.

Veronese embedding as ring isomorphism

Can every monoid be turned into a ring?

The set of the form $ m+n\sqrt{-3} $, $ m, n\in\mathbb Z $ or $ m, n $ are both halves of odd integers is a Euclidean domain

Prove every finite field is of cardinality $p^n$

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