A ring is an abelian group in addition, with the added operation (*) being distributive over addition, and 0 annihilating under multiplication. (*) is also associative. Rings don't necessarily need _multiplicative_ id, only _additive_ id. Sometimes Rings w/o ID is called a Rng (a bit of a pun).

/Joe


On Oct 7, 2009, at 4:41 PM, David Menendez wrote:

On Wed, Oct 7, 2009 at 12:08 PM, Ben Franksen <ben.frank...@online.de> wrote:

More generally, any ring with multiplicative unit (let's call it 'one') will
do.

Isn't that every ring? As I understand it, the multiplication in a
ring is required to form a monoid.

--
Dave Menendez <d...@zednenem.com>
<http://www.eyrie.org/~zednenem/>
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