Timeline for When is $A$ isomorphic to $A^3$?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2023 at 22:33 | comment | added | Garrett Ervin | @bof I believe that's frequently the case but not always: there are for example linear orders $A, B$ such that $A \times B \times B \cong A$ but $A \times B \not \cong A$. | |
| Jan 8, 2023 at 12:13 | comment | added | bof | In cases where the cube property holds, does it hold more generally that $A\cong A\times B\times C$ implies $A\cong A\times B$? | |
| Jan 6, 2023 at 18:24 | comment | added | bof | I thought the first example of a countable Boolean algebra isomorphic to its cube but not to its square was due to Shin'ichi Kinoshita, A solution of a problem of R. Sikorski, Fund. Math. 40 (1953), 39-41. impan.pl/en/publishing-house/journals-and-series/… | |
| Jan 6, 2023 at 7:50 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Aug 23, 2018 at 9:42 | comment | added | Joshua Erde | With regards to the question of Trnková about whether there exists a connected graph isomorphic to it's cube but not it's square with respect to the cartesian product, I believe the fact that there is no such graph follows from a theorem of Imrich/Miller (see for example "Weak cartesian products of graphs" by Miller) that says that every connected graph has a unique representation as a weak cartesian product of prime factors (where the weak cartesian product is a component of the cartesian product). | |
| Nov 17, 2017 at 6:52 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
added dml.cz links
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 21, 2016 at 18:32 | history | edited | Garrett Ervin | CC BY-SA 3.0 |
added 92 characters in body
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| Oct 19, 2016 at 21:26 | history | edited | Garrett Ervin | CC BY-SA 3.0 |
added 116 characters in body
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| Oct 19, 2016 at 17:50 | history | answered | Garrett Ervin | CC BY-SA 3.0 |