Joe Fredette wrote:
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.
Yes, this is how I learned it in
Daniel Fischer wrote:
Am Montag 05 Oktober 2009 16:29:02 schrieb Job Vranish:
In what way is it not a number?
If there's a natural[1] implementation of fromInteger, good.
If there isn't, *don't provide one*.
fromInteger _ = error Not sensible is better than doing something
strange.
[1]
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
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
Am Mittwoch 07 Oktober 2009 22:44:19 schrieb Joe Fredette:
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_
I was just quoting from Hungerford's Undergraduate text, but yes, the
default ring is in {Rng, Ring}, I haven't heard semirings used in
the sense of a Rng. I generally find semirings defined as a ring
structure without additive inverse and with 0-annihilation (which one
has to assume in
Am Mittwoch 07 Oktober 2009 23:51:54 schrieb Joe Fredette:
I was just quoting from Hungerford's Undergraduate text, but yes, the
default ring is in {Rng, Ring}, I haven't heard semirings used in
the sense of a Rng.
It's been looong ago, I seem to have misremembered :?
But there used to be a
Daniel Fischer wrote:
Am Mittwoch 07 Oktober 2009 23:51:54 schrieb Joe Fredette:
I generally find semirings defined as a ring
structure without additive inverse and with 0-annihilation (which one
has to assume in the case of SRs, I included it in my previous
definition because I wasn't
On Wed, Oct 07, 2009 at 08:44:27PM -0400, Jason McCarty wrote:
Daniel Fischer wrote:
Am Mittwoch 07 Oktober 2009 23:51:54 schrieb Joe Fredette:
I generally find semirings defined as a ring
structure without additive inverse and with 0-annihilation (which one
has to assume in the case
Am Donnerstag 08 Oktober 2009 03:05:13 schrieb Felipe Lessa:
On Wed, Oct 07, 2009 at 08:44:27PM -0400, Jason McCarty wrote:
Daniel Fischer wrote:
Am Mittwoch 07 Oktober 2009 23:51:54 schrieb Joe Fredette:
I generally find semirings defined as a ring
structure without additive inverse
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