Timeline for Does the set of ideals, whose Jacobson radical & nilradicals coincide, form a sublattice?
Current License: CC BY-SA 4.0
9 events
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Aug 9, 2022 at 16:06 | vote | accept | Onur Oktay | ||
Aug 9, 2022 at 16:05 | history | edited | Onur Oktay | CC BY-SA 4.0 |
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Aug 9, 2022 at 15:06 | history | edited | Onur Oktay | CC BY-SA 4.0 |
fixed the accidental false assignment of the hyperlinks.
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Aug 9, 2022 at 4:52 | answer | added | Keith Kearnes | timeline score: 2 | |
Aug 8, 2022 at 11:43 | history | edited | Onur Oktay | CC BY-SA 4.0 |
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Aug 8, 2022 at 8:27 | history | edited | Onur Oktay | CC BY-SA 4.0 |
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Aug 8, 2022 at 8:27 | comment | added | Onur Oktay | @HenrikRüping thank you for your good Samaritan approach. I'm more interested in whether $\mathcal{S}$ is closed under sums and infinite intersections of its members. I think it is also interesting if $\mathcal{S}$ is a lattice without being a sublattice of $L(R)$. Specifically, given $I,J\in\mathcal{S}$, does there exist a smallest ideal in $\mathcal{S}$ that contain $I+J$? | |
Aug 8, 2022 at 7:33 | comment | added | HenrikRüping | While I dont know the answer to this question, there is a sublety with the definition of sublattice, that occasionally causes problems. One definition for a lattice is a poset in which each subset has a greatest lower bound and a leaast upper bound. Then there are sub-posets which are also lattices for which the greatest lower bounds and least upper bounds dont agree with the ones for the big posets. For example $a\le b \le c,d \le e\le f$. In this poset the greatest lower bound of $c,d$ would be $b$, but if we look at the sub-poset given by $a,c,d,e$, it would be $a$. | |
Aug 8, 2022 at 0:00 | history | asked | Onur Oktay | CC BY-SA 4.0 |