If R is a finite integral domain, show that R is a field.
Please show steps. Thanks!
do you know what an integral domain is? do you know what a field is? look at the definitions. you need only show that the set of nonzero elements of a finite integral domain forms a group with respect to multiplication.
If R is a finite integral domain, show that R is a field.
Please show steps. Thanks!
Hi mpryal.
Pick a nonzero element in and consider the set This must be a finite set of nonzero elements; hence there exist positive integers with such that Thus Since and is an integral domain, is the multiplicative inverse of in . (Note that