Actually, in a ring multiplication doesn't always have an identity. You should follow the definition from the book contemporary abstract algebra(4th edition).
Here you've to check only one element for multiplicative identity. So if you multiply 0 with 0 then you can get 0. So 0 is multiplicative identity here
Sir zero ring R={0}.In this ring 1=0 how..??? Explain
He means that '0' is the multiplicative identity.
@@adeelali8417 yeah, perhaps he should've been clearer on that
it is a trivial set. do not think over it too much.
Actually, in a ring multiplication doesn't always have an identity. You should follow the definition from the book contemporary abstract algebra(4th edition).
Here you've to check only one element for multiplicative identity. So if you multiply 0 with 0 then you can get 0. So 0 is multiplicative identity here
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On 23:35 constant function 1 sends every element of R to itself.
no, here we are considering "1: a --> 1", so that it can be multiplicative identity for the ring