Is Z6 subring of Z12?

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

  1. abdo abdo

    abdo abdo

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    Is Z6 subring of Z12?
     
    abdo abdo, May 13, 2017
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  2. abdo abdo

    Country Boy

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    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
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  3. abdo abdo

    MathLover1

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    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
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  4. abdo abdo

    nycmathguy

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    Is this linear algebra or abstract algebra?
     
    nycmathguy, Feb 1, 2022
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  5. abdo abdo

    Country Boy

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    "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
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  6. abdo abdo

    nycmathguy

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    Thank the Lord I never have to take abstract algebra.
     
    nycmathguy, Mar 11, 2022
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