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Homework Help: Ring Theory

  1. Feb 28, 2008 #1
    1. The Problem

    If S and T are subrings of a ring R, show that S intersects T, is a subring of R.

    3. The attempt at a solution

    I don't know how to go about answering this question.
  2. jcsd
  3. Feb 28, 2008 #2
    What are the requirements for a subset of R to be a subring?
  4. Feb 28, 2008 #3
    The following axioms must be satisfied
    a) (for all or any) x,y E R implies x+(-y) E R
    b) (for all or any) x,y E R implies xy E R ( R is closed under mulitplication)

    The above are the requirements for a subring to be valid.

    This is something i got from wikipedia:

    Let R be a ring. Any intersection of subrings of R is again a subring of R. Therefore, if X is any subset of R, the intersection of all subrings of R containing X is a subring S of R. S is the smallest subring of R containing X. ("Smallest" means that if T is any other subring of R containing X, then S is contained in T.) S is said to be the subring of R generated by X. If S = R, we may say that the ring R is generated by X.

    So then does S=T?
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