Abstract Algebra Answers

Let G be the set of all real-valued functions on the real line with the binary operation given by pointwise addition of functions: If f, g ∈ G, then f + g is the function whose value at x ∈ R is f (x) + g (x), that is (f + g) (x) = f (x) + g (x). Show that G is a group.

Give any two examples of a non-cyclic group, all of whose proper subgroups are

cyclic.

Prove that [(-a,b)] is the additive inverse for [(a,b)] in the field of quotients. NOTE: these are equivalence classes

prove that [ (-a,b)] is the additive inverse for [(a,b)] in the field of quotients. remember that these are equivalence classes.

Consider {0,2,4} as a subset of Z₆. show it is a subring and does it have a unity?

Determine the elements of order 15 of U(225)

Prove that [(−a, b)] is the additive inverse for [(a, b)] in the field of quotients. Remember that these are equivalence classes .

Consider { 0,2,4} as a subset of Z₆ . show it is a subring. does it have unity?