Glossary of Ring Theory - Definition of A Ring

Definition of A Ring

Ring
A ring is a set R with two binary operations, usually called addition (+) and multiplication (*), such that R is an abelian group under addition, a monoid under multiplication, and such that multiplication is both left and right distributive over addition. Note that rings are assumed to have multiplicative identities unless otherwise noted. The additive identity is denoted by 0 and the multiplicative identity by 1.
Subring
A subset S of the ring (R,+,*) which remains a ring when + and * are restricted to S and contains the multiplicative identity 1 of R is called a subring of R.

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