Is the set F={0} a field? If so prove all axioms of field.?
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Answer:
The additive identity and multiplicative identity are both 0. They are not distinct, therefore it is not a field. No trivial ring (a ring with only one element) can be a field for this reason.
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Other answers
The additive identity and multiplicative identity are both 0. They are not distinct, therefore it is not a field. No trivial ring (a ring with only one element) can be a field for this reason.
Demiurge...
A field is a ring whose nonzero elements form a commutative group under multiplication. The non-zero elements is the empty set. A group must have an identity element, so it can't be empty. Therefore F is not a field.
freond1
A field is a ring whose nonzero elements form a commutative group under multiplication. The non-zero elements is the empty set. A group must have an identity element, so it can't be empty. Therefore F is not a field.
freond1
0 does not have a multiplicative inverse. Therefore, the set is not a field. I hope that helps. :) ILoveMaths07.
ILoveMaths07
0 does not have a multiplicative inverse. Therefore, the set is not a field. I hope that helps. :) ILoveMaths07.
ILoveMaths07
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