Stock-based compensation (Details 1) (Stock Options [Member], USD $)	12 Months Ended
Dec. 31, 2011 Y	Dec. 31, 2010 Y	Dec. 31, 2009 Y
Stock Options [Member]
Weighted-average assumptions and resulting weighted-average grant date fair values
Closing price of our common stock on grant date	$ 54.66	$ 58.32	$ 50.65
Expected volatility	23.50%	28.00%	39.60%
Expected life (in years)	5.9	6.6	4.6
Risk-free interest rate	2.50%	3.20%	2.10%
Expected dividend yield	2.00%	0.00%	0.00%
Fair value of stock options granted	$ 11.39	$ 20.97	$ 18.35

The period of time an equity-based award is expected to be outstanding. An equity-based award's expected term is generally determined based on, among other factors, the instrument's contractual term and the effects of employees' expected exercise and post-vesting employment termination behavior.

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The estimated measure of the percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period.

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