So a clearer reframing might be: “Ring is like Field, but without multiplicative inverse”. <br><br><div class="gmail_quote">On Wed, Mar 18, 2009 at 7:17 AM, Kalman Noel <span dir="ltr"><<a href="mailto:noel.kalman@googlemail.com">noel.kalman@googlemail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">Wolfgang Jeltsch schrieb:<br>
<div class="im">> Okay. Well, a monoid with many objects isn’t a monoid anymore since a monoid<br>
> has only one object. It’s the same as with: “A ring is a field whose<br>
> multiplication has no inverse.” One usually knows what is meant with this but<br>
> it’s actually wrong. Wrong for two reasons: First, because the multiplication<br>
> of a field has an inverse. Second, because the multiplication of a ring is<br>
> not forced to have no inverse but may have one.<br>
<br>
</div>“A ring is like a field, but without a multiplicative inverse” is, in my<br>
eyes, an acceptable formulation. We just have to agree that “without”<br>
here refers to the definition, rather than to the definitum.<br>
<div><br></div></blockquote></div><br>