Timeline for If $H$ is commutative and unit-cancellative, then so is the monoid of non-empty ideals of $H$
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| Apr 28, 2017 at 6:18 | comment | added | Salvo Tringali | Btw, I've just realized that I had essentially answered this question in the edit of April 25 at 23:55 to mathoverflow.net/questions/267977 (using the example of the monoid of non-negative rationals under addition). Maybe I should stop posting questions when it's so late in the night... | |
| Apr 28, 2017 at 6:09 | comment | added | Salvo Tringali | Right. In hindsight (and with a fresher mind) this is kind of obvious: All the monoids mentioned in your answer are divisibile, Dedekind-finite, commutative monoids where the group of units is a proper submonoid. In particular, "being Dedekind-finite & not a group" is a necessary and sufficient condition for the relative complement of the units to be a non-empty ideal (as already noted in mathoverflow.net/questions/267977), while "being Dedekind-finite & divisible" implies that the relative complement of the units is an idempotent ideal. | |
| Apr 28, 2017 at 6:01 | vote | accept | Salvo Tringali | ||
| Apr 28, 2017 at 0:49 | history | answered | R. van Dobben de Bruyn | CC BY-SA 3.0 |