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Identity in subring

  1. Oct 27, 2008 #1
    should the subring inherit the same multiplicative identity of the original ring? assuming multiplicative identity is required in the definition of ring.

    according to the book (Rotman's), [tex]1\in S[/tex] is required. But, does it mean S contains the same multiplicative identity, or contains its own multiplicative identity?

    Consider Z_6 defined on Z by taking mod 6. And its subset S={3k| k is integers} equipped with the same operations as in Z_6.
    S is itself a ring, having multiplicative identity 3. I'm wondering if S is called a subring of Z_6?
     
  2. jcsd
  3. Oct 27, 2008 #2

    morphism

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    It's a matter of convention. Most authors, when they require rings to have a multiplicative identity, will stipulate that a subring must have the same multiplicative identity as the ring.
     
  4. Oct 28, 2008 #3
    Thanks a lot!
     
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