Question

Division Algorithm Theorem for Commutative Rings with Unity - existence and uniqueness?

score 192 · Answer 1 · 2026-04-13 04:49:41

192

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Division Algorithm Theorem for Commutative Rings with Unity - existence and uniqueness?

Published on 13 Apr 2026 - 4:49

score 259 · Answer 2 · 2026-04-15 10:17:13

259

Views

Suppose that $R$ is a ring and $a,b\in R$. Prove that if $a+b = ab$, then $ab=ba$.

Published on 15 Apr 2026 - 10:17

score 130 · Answer 3 · 2026-04-15 14:39:38

130

Views

Examples of inite regular rings that are not semi-simple rings

Published on 15 Apr 2026 - 14:39

score 54 · Answer 4 · 2026-04-16 14:21:49

If for $x\in R$, either $x$ or $x-1$ is regular then for (prime) ideals $I$ and $J$ of $R$ consisting of zero divisors, $I+J\ne R$.

score 105 · Answer 5 · 2026-03-25 17:19:47

105

Views

Redundancy Hungerford: Ex. 4.1.13 & 4.1.15, zero divisors and units

Published on 25 Mar 2026 - 17:19

score 41 · Answer 6 · 2026-03-26 02:53:00

41

Views

Rings with rectangles with same perimeter but different surface

Published on 26 Mar 2026 - 2:53

score 133 · Answer 7 · 2026-04-16 07:35:28

133

Views

Prove that for $R$ a ring with unity and $M_R$ an $R$-module, the set of elements in $M$ which annihilate $I^k$, $I$ an ideal, is a submodule

Published on 16 Apr 2026 - 7:35

score 33 · Answer 8 · 2026-04-16 07:23:49

33

Views

Products of matrices over non-fields

Published on 16 Apr 2026 - 7:23

score 290 · Answer 9 · 2026-04-11 14:19:43

290

Views

Prime ideal lies above

Published on 11 Apr 2026 - 14:19

score 139 · Answer 10 · 2026-04-14 17:27:43

139

Views

Corollary of Nakayama's Lemma

Published on 14 Apr 2026 - 17:27

score 101 · Answer 11 · 2026-05-11 09:09:47

101

Views

A semiring isomorphic to a cartesian product of two semirings

Published on 11 May 2026 - 9:09

score 309 · Answer 12 · 2026-04-18 03:04:58

309

Views

$S$ subring of $R$ implies $\mathrm{rank}_R M\leq \mathrm{rank}_S M$?

Published on 18 Apr 2026 - 3:04

score 131 · Answer 13 · 2026-05-10 17:17:48

131

Views

Prove that an ideal of a subring of $\mathbb{Q}$ is principal

Published on 10 May 2026 - 17:17

score 59 · Answer 14 · 2026-05-05 08:34:56

59

Views

A question about integral ring extension

Published on 05 May 2026 - 8:34

score 155 · Answer 15 · 2026-04-12 14:06:12

155

Views

Prime ideal and ring of integers

Published on 12 Apr 2026 - 14:06

List Question

Division Algorithm Theorem for Commutative Rings with Unity - existence and uniqueness?

Suppose that $R$ is a ring and $a,b\in R$. Prove that if $a+b = ab$, then $ab=ba$.

Examples of inite regular rings that are not semi-simple rings

If for $x\in R$, either $x$ or $x-1$ is regular then for (prime) ideals $I$ and $J$ of $R$ consisting of zero divisors, $I+J\ne R$.

Redundancy Hungerford: Ex. 4.1.13 & 4.1.15, zero divisors and units

Rings with rectangles with same perimeter but different surface

Prove that for $R$ a ring with unity and $M_R$ an $R$-module, the set of elements in $M$ which annihilate $I^k$, $I$ an ideal, is a submodule

Products of matrices over non-fields

Prime ideal lies above

Corollary of Nakayama's Lemma

A semiring isomorphic to a cartesian product of two semirings

$S$ subring of $R$ implies $\mathrm{rank}_R M\leq \mathrm{rank}_S M$?

Prove that an ideal of a subring of $\mathbb{Q}$ is principal

A question about integral ring extension

Prime ideal and ring of integers

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