Question

How to prove that $\text{lcm}(zx, zy)=z \text{lcm}(x, y)$?

score 144 · Answer 1 · 2018-09-03 14:53:41

144

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How to prove that $\text{lcm}(zx, zy)=z \text{lcm}(x, y)$?

Published on 03 Sep 2018 - 14:53

score 874 · Answer 2 · 2018-09-03 15:10:36

874

Views

If $R$ is an integral domain then $R[x]$ forms an integral domain

Published on 03 Sep 2018 - 15:10

score 1.7k · Answer 3 · 2026-03-25 17:38:49

1.7k

Views

How to factor polynomials in $\mathbb{Z}_{n}[x]$

Published on 25 Mar 2026 - 17:38

score 66 · Answer 4 · 2026-03-28 14:36:55

66

Views

Every set with more than $k$ elements is dependent

Published on 28 Mar 2026 - 14:36

score 53 · Answer 5 · 2026-03-25 07:49:22

53

Views

Every algebra could be decomposed into a part with unit, and without a unit. Question on uniqueness proof.

Published on 25 Mar 2026 - 7:49

score 88 · Answer 6 · 2026-03-28 01:06:34

88

Views

The strictly upper triangular "subalgebra" of $M_n(K)$ is not unital?

Published on 28 Mar 2026 - 1:06

score 1.8k · Answer 7 · 2026-03-29 10:15:14

1.8k

Views

Proof nilradical is intersection of prime ideals.

Published on 29 Mar 2026 - 10:15

score 46 · Answer 8 · 2026-03-22 12:47:17

46

Views

Projective Nullstellensatz and regular rings

Published on 22 Mar 2026 - 12:47

score 69 · Answer 9 · 2018-09-06 00:55:40

69

Views

Let $R$ a commutative ring and $I$ and ideal of $R$,how i can show that if $\sqrt{I}=R$ then $I=R$

Published on 06 Sep 2018 - 0:55

score 204 · Answer 10 · 2026-03-29 08:18:29

204

Views

Problem understanding the concept of principal ideal

Published on 29 Mar 2026 - 8:18

score 3k · Answer 11 · 2018-09-06 17:42:07

3k

Views

Prove $\langle x^2+1\rangle$ is maximal in $R[x]$

Published on 06 Sep 2018 - 17:42

score 99 · Answer 12 · 2026-03-25 11:27:17

99

Views

Show that if $R$ is a ring with a single ideal prime minimal $\neq(0)$ then $R$ has non-trivial nilpotent elements

Published on 25 Mar 2026 - 11:27

score 1.1k · Answer 13 · 2018-09-07 04:42:40

1.1k

Views

To prove that a set is the smallest ideal of R

Published on 07 Sep 2018 - 4:42

score 73 · Answer 14 · 2018-09-08 01:02:53

73

Views

A ring $R$ with a product that is non commutative, non associative, and with no unit element.

Published on 08 Sep 2018 - 1:02

score 213 · Answer 15 · 2026-03-31 03:26:50

213

Views

In studying abstract algebra, is vector space structure important?

Published on 31 Mar 2026 - 3:26

List Question

How to prove that $\text{lcm}(zx, zy)=z \text{lcm}(x, y)$?

If $R$ is an integral domain then $R[x]$ forms an integral domain

How to factor polynomials in $\mathbb{Z}_{n}[x]$

Every set with more than $k$ elements is dependent

Every algebra could be decomposed into a part with unit, and without a unit. Question on uniqueness proof.

The strictly upper triangular "subalgebra" of $M_n(K)$ is not unital?

Proof nilradical is intersection of prime ideals.

Projective Nullstellensatz and regular rings

Let $R$ a commutative ring and $I$ and ideal of $R$,how i can show that if $\sqrt{I}=R$ then $I=R$

Problem understanding the concept of principal ideal

Prove $\langle x^2+1\rangle$ is maximal in $R[x]$

Show that if $R$ is a ring with a single ideal prime minimal $\neq(0)$ then $R$ has non-trivial nilpotent elements

To prove that a set is the smallest ideal of R

A ring $R$ with a product that is non commutative, non associative, and with no unit element.

In studying abstract algebra, is vector space structure important?

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