True or False: Any ring must be commutative with identity.
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- Let R be a commutative ring with characteristic 2. Show that each of the following is true for all x,yR a. (x+y)2=x2+y2 b. (x+y)4=x4+y4True or false Label each of the following statements as either true or false. A ring homomorphism from a ring To a ring must preserve both ring operations.True or False Label each of the following statements as either true or false. 4. If a ring has characteristic zero, then must have an infinite number of elements.
- 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?True or False Label each of the following statements as either true or false. If one element in a ring R has a multiplicative inverse, then all elements in R must have multiplicative inverses.Label each of the following statements as either true or false. Every subring of a ring R is an idea of R.