Timeline for Examples of natural algebraic irreflexive relations
Current License: CC BY-SA 4.0
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| Oct 8 at 8:51 | comment | added | Zhen Lin | Thank you! I shall have to remember the name of Mal'cev... | |
| Oct 7 at 21:33 | history | edited | Keith Kearnes | CC BY-SA 4.0 |
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| Oct 7 at 21:16 | history | edited | Keith Kearnes | CC BY-SA 4.0 |
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| Oct 7 at 13:54 | comment | added | Zhen Lin | Sorry, a minor point, but I don't quite understand how you obtain a chain of identities of the form claimed. I agree there is some chain of identities that witnesses the hypothesis that $(0, x)$ is in the congruence, and as far as I can tell it seems the exact form does not really matter, but it would be nice to know how concrete we can be about the congruence generated by a pair of elements. | |
| Oct 5 at 12:59 | comment | added | Zhen Lin | I think I see how this can be generalised: basically, we are defining a natural algebraic irreflexive relation on the free algebra on no generators and then pushing it forward to all algebras. In some sense these are "constant", and there can be quite a lot of them because the class of these is downward-closed and also closed under union... (In particular, there is a maximal one, both among the "constant" ones and in general. I think the example for commutative rings is maximal.) | |
| Oct 5 at 11:24 | comment | added | Zhen Lin | This is even representable! Apparently my intuition was not quite right… | |
| Oct 5 at 4:29 | history | edited | Keith Kearnes | CC BY-SA 4.0 |
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| Oct 5 at 4:07 | history | answered | Keith Kearnes | CC BY-SA 4.0 |