Is Z6 subring of Z12?

[abdo abdo]

Is Z6 subring of Z12?

 

[Country Boy]

I'm not sure I would say it IS a subgroup but it is isomorphic to the subgroup {0, 2, 4, 6, 8, 10}.

 

[MathLover1]

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.

 

[nycmathguy]

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.

Is this linear algebra or abstract algebra?

 

[Country Boy]

"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".

 

[nycmathguy]

"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".

Thank the Lord I never have to take abstract algebra.