Timeline for Do you know of any indecomposable ring that has no isolated elements and is neither reversible, nor integral, nor nilpotent, nor unitary?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 23, 2022 at 2:41 | vote | accept | José María Grau Ribas | ||
| Sep 22, 2022 at 17:51 | comment | added | Pace Nielsen | Alternatively, just replace $F$ with $2\mathbb{Z}$, and adjust things accordingly. | |
| Sep 22, 2022 at 17:50 | comment | added | Pace Nielsen | @rschwieb Good point. If they don't want it unital, they can add a new variable $z$, commuting with $x$ and $y$, and take the nonunital subring generated by $x,y,z$. This ring won't be unital, since it is graded by degree. It won't be nilpotent since $z$ isn't nilpotent. We didn't add any new idempotents, so it is still indecomposable. | |
| Sep 22, 2022 at 17:33 | comment | added | rschwieb | There's some ambiguity: the title asks for "not unitary" whereas the body says "not finite unital." This is a great answer for the body question, at least (which I guess is probably the intended one.) | |
| Sep 21, 2022 at 22:46 | history | answered | Pace Nielsen | CC BY-SA 4.0 |