On Thu, Apr 5, 2012 at 1:20 AM, Tom Bachmann <[email protected]> wrote:
>
> In my background "ring" is synonymous with commutative unital ring. As far
> as I know there is quite a large body of mathematics (mainly related to
> representation theory) devoted to the study of non-commutative rings as
> well.

Yeah, I can confirm that.  The institute I'm currently doing a bit of
research at has a team of people who work specifically on
non-commutative algebras.  While I don't really know what exactly
there are (or were) doing, I know that non-commutative algebras arise
naturally somewhere around formal languages.

> All of this is really just nitpick for saying: while some in contexts rings
> without identity are fine, we should not be required to treat ideals in this
> way.

Yes, now that we've found the confusing point in the definition of
ring vs. unital ring, I agree with the statement.

Sergiu

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