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Math Help - factor rings

  1. #1
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    factor rings

    Draw up an addition and a multiplication table for the factor ring 2
    Z/8Z.What known ring is 2Z/8Z isomorphic

    to?
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  2. #2
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    Draw up an addition and a multiplication table for the factor ring 2
    Z/8Z.What known ring is 2Z/8Z isomorphic to
    If \phi :R_1\to R_2 is an isomorphism of commutative rings and I_1 is an ideal of R_1 then \phi (I_1) = I_2 is an ideal of R_2 and furthermore R_1/I_1\simeq R_2/I_2. Define \phi: 2\mathbb{Z}\to \mathbb{Z} by \phi(x) = \tfrac{x}{2}. This is an isomorphism. Let I_1 = 8\mathbb{Z}, this is an ideal of 2\mathbb{Z}. Note that I_2 = \phi (I_1) = 4\mathbb{Z}. Thus, 2\mathbb{Z}/I_1 \simeq \mathbb{Z}/I_2 = \mathbb{Z}_4.
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