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Math Help - abstract algebra

  1. #1
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    abstract algebra

    how is it possible for a subring S of a ring R to have a unity, even if R has no unity?

    wouldn't the unity in S have to be the unity in R?
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  2. #2
    Senior Member JaneBennet's Avatar
    Joined
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    Well, you could have a ring R with no unity but contains an element a\ne0 such that a+a=0 and a^2=a; then S=\{0,a\} would be a subring with unity (a would be a unity in S even though it is not a unity in R). Unfortunately I canít think of a concrete example of such a ring/subring Ė but Iím guessing itís possible.
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