The definition of a field {F; +, } consisting of a set F with elements called scalars on which two operations are defined, + and - Two fields are {C; +, :} and {R; +, } with the usual addition and multiplication operations. These fields are simply denoted by C and R. Another field is the field of rational functions with real coefficients R(s). (a) which 1R(4) is also an identity element. What is the identity element, 1R(«) of R(s)? Give three subsets of R(s) for

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The definition of a field {F; +, } consisting of a set F with elements called scalars on which two
operations are defined, + and - Two fields are {C; +, :} and {R; +, } with the usual addition and
multiplication operations. These fields are simply denoted by C and R. Another field is the field of
rational functions with real coefficients R(s).
(a)
What is the identity element, 1R(6) of R(s)? Give three subsets of R(s) for
which IR(s) is also an identity element.
Transcribed Image Text:The definition of a field {F; +, } consisting of a set F with elements called scalars on which two operations are defined, + and - Two fields are {C; +, :} and {R; +, } with the usual addition and multiplication operations. These fields are simply denoted by C and R. Another field is the field of rational functions with real coefficients R(s). (a) What is the identity element, 1R(6) of R(s)? Give three subsets of R(s) for which IR(s) is also an identity element.
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