Check that if you add (or multiply) two fractions in Z(2) you get a fraction that...

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Check that if you add (or multiply) two fractions in Z(2) you get a fraction that is not an arbitrary rational number but one that also lives in Z(2). What role does the fact that the denominators are odd play in ensuring this? (The role of the odd denominators is rather crucial; make sure that you understand it!) Question 2.15.3 Why do associativity and distributivity follow from the fact that Z(2) ≤Q? Question 2.15.4 Do the other ring axioms hold? Check! Does Z(2) contain 2/6? Check that if you add (or multiply) two fractions in Z(2) you get a fraction that is not an arbitrary rational number but one that also lives in Z(2). What role does the fact that the denominators are odd play in ensuring this? (The role of the odd denominators is rather crucial; make sure that you understand it!) Question 2.15.3 Why do associativity and distributivity follow from the fact that Z(2) ≤Q? Question 2.15.4 Do the other ring axioms hold? Check! Does Z(2) contain 2/6?

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In Z2 also known as the ring of integers modulo 2 the elements are congruence classes 0 and 1 Addition and multiplication in Z2 are defined modulo 2 meaning that the results are reduced to either 0 or ... View the full answer