Timeline for Rings with right inverses
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2010 at 2:45 | comment | added | Peter LeFanu Lumsdaine | @Pete: what I always have the most trouble with is remembering which way round the subscripts for matrix entries go :-) But I guess I've been doing category theory long enough now that function-composition conventions are burned into my brain… | |
| Oct 17, 2010 at 2:53 | comment | added | Pete L. Clark | @Peter: yes, it looks we are using left/right inverse in different senses when the ring operation is function composition. As I say though, no matter. (I'm willing to believe that your convention is the right one. I am mildly dyslexic on this kind of mathematical issue: e.g. I used to have a hard time remembering which were left and which were right cosets.) | |
| Oct 15, 2010 at 16:29 | comment | added | Peter LeFanu Lumsdaine | @Pete: ah, of course; I guess the precise differences are just rescaling and a change of scalars from $\mathbb{Z}$ to $\mathbb{R}$. Though I'm confused about what you say regarding the order of the product: I also read $x \cdot y$ as “first $y$ then $x$”; maybe we’re using left/right inverse opposite ways round? As I understand the convention, if $l\cdot r = 1$, then $l$ is a left inverse for $r$, and $r$ a right inverse for $l$. So a left inverse is epimorphic, like the left shift or the derivative? | |
| Oct 15, 2010 at 13:54 | comment | added | Pete L. Clark | @Peter: Ironically, I think your example is essentially the same as mine but with the other convention on the order of the product x*y: for me, since these are functions, I read them as first do y, then do x, but your convention makes just as much sense. Thus we are working in opposite rings, as in my answer above. [To be precise, your ring is not literally the same as mine, but they are similar, and it is well known that the derivative is a rescaled shift operator.] | |
| Oct 15, 2010 at 5:17 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 2.5 |