![]() ![]() (This structure is called a monoid.)Ī commutative ring is a field when all nonzero elements have multiplicative inverses. The binary operation of multiplication is associative and it does have an identity 1, but some elements like 0 do not have inverses. If you forget about addition, then a ring does not become a group with respect to multiplication. If you forget about multiplication, then a ring becomes a group with respect to addition (the identity is 0 and inverses are negatives). The main difference between groups and rings is that rings have two binary operations (usually called addition and multiplication) instead of just one binary operation. You're right to think that the definitions are very similar. BBischof BBischof $endgroup$ $begingroup$ ![]()
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