Homework Help: Ring Theory

1. Feb 28, 2008

lostinmath08

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. Feb 28, 2008

Mystic998

What are the requirements for a subset of R to be a subring?

3. Feb 28, 2008

lostinmath08

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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