On Wed, Apr 4, 2012 at 10:19 PM, Tom Bachmann <[email protected]> wrote: >>> I don't think that makes sense. Ideals have no natural multiplicative >>> unit, >>> whereas a type of ring I tend to think of has (admittedly, this may >>> sometimes be relaxed). >> >> >> I'm not sure I see your point here; indeed, an ideal of ring with a >> multiplicative unit need not necessarily include the unit, but this >> doesn't make it less of a ring. >> > > In my book it does. Of course there are non-commutative rings, and rings > without units, but for me "ring" without further qualifications means > "unital commutative ring, with homomorphism respecting the identity". And > while I agree that considering rings without a multiplicative identity > probably makes sense sometims, I don't think any commutative algebraist will > be particularly happy with a framework where ideals are non-unital > subrings...
Since I'm not exactly expert in ring theory, I tried to look up examples of non-unital rings, and I have come over this curious (for me, at least) Wikipedia page: http://en.wikipedia.org/wiki/Pseudo-ring#Examples It looks like rings without the multiplicative unit do have important use-cases, but I obviously don't claim ultimate authority. Sergiu -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
