Timeline for Matrix ring isomorphisms of different sizes
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24 at 20:52 | vote | accept | Pace Nielsen | ||
| Feb 24 at 8:23 | answer | added | Jeremy Rickard | timeline score: 14 | |
| Feb 23 at 15:43 | comment | added | Jeremy Rickard | Or $(\mathbb{N}\setminus\{1\},+)$, as some people prefer to call that monoid. | |
| Feb 23 at 15:32 | comment | added | Pace Nielsen | @JeremyRickard Ah, so we take the commutative monoid generated by two elements $a,b$, subject to the single relation $a+a=b+b+b$. Taking $R$ to be the endomorphism ring of the projective module corresponding to $a$, and taking $S$ to be the endomorphism ring of the projective module corresponding to $b$, we are done (because, clearly, no element $c$ exists with $6c=2a=3b$). | |
| Feb 23 at 15:16 | comment | added | Jeremy Rickard | I don’t have time just now to write a full answer, but doesn’t this follow from Bergman’s theorem that every monoid is the monoid of finitely generated projective modules for some ring unless it obviously isn’t? | |
| Feb 23 at 13:54 | history | asked | Pace Nielsen | CC BY-SA 4.0 |