Prove or disprove any four of the following 2. Any field is a division ring.
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- Label each of the following statements as either true or false. The field of real numbers is complete.Consider the set S={ [ 0 ],[ 2 ],[ 4 ],[ 6 ],[ 8 ],[ 10 ],[ 12 ],[ 14 ],[ 16 ] }18. Using addition and multiplication as defined in 18, consider the following questions. Is S a ring? If not, give a reason. Is S a commutative ring with unity? If a unity exists, compare the unity in S with the unity in 18. Is S a subring of 18? If not, give a reason. Does S have zero divisors? Which elements of S have multiplicative inverses?If R1 and R2 are subrings of the ring R, prove that R1R2 is a subring of R.
- 37. Let and be elements in a ring. If is a zero divisor, prove that either or is a zero divisor.True or false Label each of the following statements as either true or false. 7. For the quotient ring of by the ideal is .True or False Label each of the following statements as either true or false. The characteristic of a ring is the positive integer such that for all in.