Re: ring/field/algebra

In article <1130299296.031977.273270@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
ken.quirici@xxxxxxxxxx <ken.quirici@xxxxxxxxxx> wrote:
>
>Arturo Magidin wrote:
>> >
>> Your correction was unnecessary. Their definition states that a ring
>> is a set with two binary operators, + and *. By definition, a binary
>> operator on a set S is a function from S x S to S; that means that it
>> is "closed" in the sense you mean, BY DEFINITION. Adding the statement
>> that the sum of two elements is again an element of the set is
>> superfluous.

>That's true. However the definition of group explicitly includes
>the closure property, while the definition of ring includes all the
>properties except the closure property.

Yes. The inclusion of closure in the description of group is superfluous.

> Pedagogically speaking,

Mathworld is not meant to be pedagogic.


--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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