Talk:Grothendieck group

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[edit] Correct title?

Is it really correct to call the simple construction (of the universal covering group of a monoid) the Grothendieck group? Every time I've seen it presented, it was done so without the Grothendieck name attached to it, whereas the Grothendiek group is only discussed for Abelian categories, and not just on plain monoids (which is more simply the "universal abelian group" or something like that. linas 19:36, 1 April 2007 (UTC)

This came up in discussion on Talk:Semigroup. I would like to expand on the definition of the simpler thing, which I'm afraid might make the article very long, kind of drowning out the bit about the abelian category. Thus, perhaps, would it be agreeable to split this article into two, assuming that a name can be found for the "simpler thing"? (I don't know what it should be called, and notes that I have do not give it a name). linas 19:42, 1 April 2007 (UTC)

All of which is contradicted by the planetmath article, which defines only the "simpler" thing. Oh well. linas 13:07, 2 April 2007 (UTC)

The "simpler thing" is known as "group completion (of a monoid)" DesolateReality (talk) 12:24, 26 March 2009 (UTC)

[edit] Cancellation

It seems pretty obvious that cancellation is necessary for this construction. So why is there no mention of it? Thehotelambush (talk) 22:43, 30 September 2008 (UTC)

Never mind, the +k accounts for this. Thehotelambush (talk) 04:27, 9 May 2009 (UTC)