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Question 1195280: Determine the characteristic of the ring.
(P(∅), Δ,∩)
I think it has no characteristic based on the definition.
In the powerset of the empty set
additive identity (0)= {}
multiplicative identity (1)= {}
so 0=1
Please help. Thank you.
These are the definition
char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0).
If this sum never reaches the additive identity the ring is said to have characteristic zero.
The ring of integers modulo n has characteristic n
If 0=1 it says to have no characteristic.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
On characteristic of rings in Algebra see this Wikipedia article
https://en.wikipedia.org/wiki/Characteristic_(algebra)#:~:text=In%20mathematics%2C%20the%20characteristic%20of,the%20additive%20identity%20(0).
I do not think that searching/investigating of a characteristic of a ring which is an empty set
would be of any interest.
It is the same as if you search for a penny in a pocket while there is no penny there - - - and you know about it . . .
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