Given a
ring (
R, +, *), we say that a
subset S of
R is a
subring thereof if it is a ring under the restriction of + and * thereto, and contains the same unity as
R. A subring is just a
subgroup of (
R, +) which contains 1 and is closed under multiplication.
Every ring has a unique smallest subring, isomorphic to either the integers Z or some modular arithmetic Zn.
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