Chapter 3, Rings
The zero ring is a subring of every ring. As with subspaces of vector spaces, it is not hard to check that a subset is a subring as most axioms are inherited from the ring. Theorem 3.2. Let S be a subset of a ring R. S is a subring of R i the following conditions all hold: (1) S is closed under addition and multiplication. (2) 0R 2 S.
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