# Is Z6 subring of Z12?

Discussion in 'Linear and Abstract Algebra' started by abdo abdo, May 13, 2017.

1. ### abdo abdo

Joined:
May 13, 2017
Messages:
1
0
Is Z6 subring of Z12?

abdo abdo, May 13, 2017

2. ### Country Boy

Joined:
Dec 15, 2021
Messages:
157
38
I'm not sure I would say it IS a subgroup but it is isomorphic to the subgroup {0, 2, 4, 6, 8, 10}.

Country Boy, Jan 31, 2022

3. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,883
Z6 = {0, 1, 2, 3, 4, 5} is not a subring of Z12 since it is not closed under addition
mod 12: 5 + 5 = 10 in Z12 and 10 is not element of Z6.

MathLover1, Jan 31, 2022
nycmathguy likes this.
4. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
420
Is this linear algebra or abstract algebra?

nycmathguy, Feb 1, 2022
5. ### Country Boy

Joined:
Dec 15, 2021
Messages:
157
38
"Linear Algebra" involves specifically "vector spaces" (abstract mathematical definition, not "Physics" vectors) and "linear transformations" between them. "Abstract algebra" involves "groups", "rings", "fields" and "homomorphisms" and "isomorphisms" between them.

Since this problem is asking specifically about rings, it is a problem in "abstract algebra".

Country Boy, Mar 10, 2022
nycmathguy likes this.

Joined:
Jun 27, 2021
Messages:
5,386