Timeline for Are there axioms satisfied in commutative rings and distributive lattices but not satisfied in commutative semirings?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2020 at 12:31 | vote | accept | Zhen Lin | ||
| Sep 10, 2020 at 12:00 | history | became hot network question | |||
| Sep 10, 2020 at 11:34 | answer | added | Andrej Bauer | timeline score: 26 | |
| Sep 10, 2020 at 9:44 | comment | added | Zhen Lin | Very nice! That axiom says that for a ring or a distributive lattice $(-) + z$ and $(-) \times z$ are jointly injective, which seems to be worth thinking about. It fails in $\mathbb{N} \cup \{ +\infty \}$ (which is a semiring if we define $0 \times {+ \infty} = 0$). I will accept that as answer. | |
| Sep 10, 2020 at 9:14 | comment | added | François G. Dorais | How about $x+z=y+z, x\times z = y \times z \vdash x = y$? There should be a rig where that doesn't hold, but it is true in every commutative ring and every distributive lattice. | |
| Sep 10, 2020 at 5:49 | history | edited | Zhen Lin | CC BY-SA 4.0 |
added 61 characters in body
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| Sep 10, 2020 at 4:00 | history | asked | Zhen Lin | CC BY-SA 4.0 |