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    Subring R of integral domain D is a subdomain of D.

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    Modern Algebra
    Ring Theory
    Subrings
    Integral Domain

    1) If D is an integral domain and R< = D is a subring of D with unity, show that R is a subdomain of D.
    This amounts to showing that 1subR and 1subD are unities from R and D respectively

    2) Give an example with D not integral domain where 1subR =/= 1 sub D
    (Hint: consider Rsub1 X Rsub2. Warning Rsub1 is not a subring of Rsub1 X Rsub2; it's not even a subset of it)

    Note : R <= D means R is a subring of D
    1subR means 1 is element of R
    1subD means 1 is element of D
    Rsub1 mean that R subscrip1
    Rsub1 X Rsub2 means cross product.

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    https://brainmass.com/math/integrals/subring-integral-domain-subdomain-35045

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    Modern Algebra
    Ring Theory
    Subrings
    Integral Domain

    1) If D ...

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