Timeline for ($\oplus$, $\otimes$) is a semiring. If $\otimes$ = +, what are the possible operators $\oplus$?
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| Jul 24, 2016 at 20:30 | comment | added | Gerhard Paseman | No. Average (a+b)/2 left and right distributes, but is not associative. plus itself associates, but does not distribute. Your logsumexp and max and min are the ones I can think of. I suspect there are noncontinuous examples ( think of a Hamel basis ) but I don't have anything explicit at present. Gerhard "Having Everything Isn't Having Something" Paseman, 2016.07.24. | |
| Jul 24, 2016 at 19:49 | comment | added | rafaelcosman | Can you give a specific example of an operator for $\oplus$? | |
| Jul 24, 2016 at 19:25 | history | answered | Gerhard Paseman | CC BY-SA 3.0 |