How to represent the variation of electrical resistance with frequency for ideal circuit elements?
An ideal element has no parasitics.
\$\newcommand{\parallelsum}{\mathbin{\|}} \$  

Resistor: \$ Z = R_{ideal} \$
Inductor: \$ Z = j\omega L_{ideal} \$
Capacitor: \$ Z = \frac{1}{C_{ideal}*j\omega} \$  

Real elements have parasitics, why? Because components don't superconduct, they all have some kind of metal in them and the metal has inductance and resistance. In most cases this can be ignored, but at high frequencies the effects of the parasitics become apparent. 

Resistor: \$ Z = R_{ideal}\parallelsum \frac{1}{C_{par}*j\omega} +j\omega L_{series} \$
Inductor: \$ Z = j\omega L_{ideal}\parallelsum \frac{1}{C_{par}*j\omega} + R_{series} \$
Capacitor: \$ Z = \frac{1}{C_{ideal}*j\omega}+j\omega L_{series}+R_{series}  \$ 

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Source: EMC Complicance Mag